TLDR: brew install postgresql@8.4.4 See answer below for more details.

*(I’ve re-edited my answer to give a more thorough workflow for installing/using older software versions with homebrew. Feel free to add a note if you found the old version better.)

Let’s start with the simplest case:

1) Check, whether the version is already installed (but not activated)

When homebrew installs a new formula, it puts it in a versioned directory like /usr/local/Cellar/postgresql/9.3.1. Only symbolic links to this folder are then installed globally. In principle, this makes it pretty easy to switch between two installed versions. (*)

If you have been using homebrew for longer and never removed older versions (using, for example brew cleanup), chances are that some older version of your program may still be around. If you want to simply activate that previous version, brew switch is the easiest way to do this.

Check with brew info postgresql (or brew switch postgresql <TAB>) whether the older version is installed:

$ brew info postgresql
postgresql: stable 9.3.2 (bottled)
http://www.postgresql.org/
Conflicts with: postgres-xc
/usr/local/Cellar/postgresql/9.1.5 (2755 files, 37M)
  Built from source
/usr/local/Cellar/postgresql/9.3.2 (2924 files, 39M) *
  Poured from bottle
From: https://github.com/Homebrew/homebrew/commits/master/Library/Formula/postgresql.rb
# … and some more

We see that some older version is already installed. We may activate it using brew switch:

$ brew switch postgresql 9.1.5
Cleaning /usr/local/Cellar/postgresql/9.1.5
Cleaning /usr/local/Cellar/postgresql/9.3.2
384 links created for /usr/local/Cellar/postgresql/9.1.5

Let’s double-check what is activated:

$ brew info postgresql
postgresql: stable 9.3.2 (bottled)
http://www.postgresql.org/
Conflicts with: postgres-xc
/usr/local/Cellar/postgresql/9.1.5 (2755 files, 37M) *
  Built from source
/usr/local/Cellar/postgresql/9.3.2 (2924 files, 39M)
  Poured from bottle
From: https://github.com/Homebrew/homebrew/commits/master/Library/Formula/postgresql.rb
# … and some more

Note that the star * has moved to the newly activated version

(*) Please note that brew switch only works as long as all dependencies of the older version are still around. In some cases, a rebuild of the older version may become necessary. Therefore, using brew switch is mostly useful when one wants to switch between two versions not too far apart.

2) Check, whether the version is available as a tap

Especially for larger software projects, it is very probably that there is a high enough demand for several (potentially API incompatible) major versions of a certain piece of software. As of March 2012, Homebrew 0.9 provides a mechanism for this: brew tap & the homebrew versions repository.

That versions repository may include backports of older versions for several formulae. (Mostly only the large and famous ones, but of course they’ll also have several formulae for postgresql.)

brew search postgresql will show you where to look:

$ brew search postgresql
postgresql
homebrew/versions/postgresql8    homebrew/versions/postgresql91
homebrew/versions/postgresql9    homebrew/versions/postgresql92

We can simply install it by typing

$ brew install homebrew/versions/postgresql8
Cloning into '/usr/local/Library/Taps/homebrew-versions'...
remote: Counting objects: 1563, done.
remote: Compressing objects: 100% (943/943), done.
remote: Total 1563 (delta 864), reused 1272 (delta 620)
Receiving objects: 100% (1563/1563), 422.83 KiB | 339.00 KiB/s, done.
Resolving deltas: 100% (864/864), done.
Checking connectivity... done.
Tapped 125 formula
==> Downloading http://ftp.postgresql.org/pub/source/v8.4.19/postgresql-8.4.19.tar.bz2
# …

Note that this has automatically tapped the homebrew/versions tap. (Check with brew tap, remove with brew untap homebrew/versions.) The following would have been equivalent:

$ brew tap homebrew/versions
$ brew install postgresql8

As long as the backported version formulae stay up-to-date, this approach is probably the best way to deal with older software.

3) Try some formula from the past

The following approaches are listed mostly for completeness. Both try to resurrect some undead formula from the brew repository. Due to changed dependencies, API changes in the formula spec or simply a change in the download URL, things may or may not work.

Since the whole formula directory is a git repository, one can install specific versions using plain git commands. However, we need to find a way to get to a commit where the old version was available.

a) historic times

Between August 2011 and October 2014, homebrew had a brew versions command, which spat out all available versions with their respective SHA hashes. As of October 2014, you have to do a brew tap homebrew/boneyard before you can use it. As the name of the tap suggests, you should probably only do this as a last resort.

E.g.

$ brew versions postgresql
Warning: brew-versions is unsupported and may be removed soon.
Please use the homebrew-versions tap instead:
  https://github.com/Homebrew/homebrew-versions
9.3.2    git checkout 3c86d2b Library/Formula/postgresql.rb
9.3.1    git checkout a267a3e Library/Formula/postgresql.rb
9.3.0    git checkout ae59e09 Library/Formula/postgresql.rb
9.2.4    git checkout e3ac215 Library/Formula/postgresql.rb
9.2.3    git checkout c80b37c Library/Formula/postgresql.rb
9.2.2    git checkout 9076baa Library/Formula/postgresql.rb
9.2.1    git checkout 5825f62 Library/Formula/postgresql.rb
9.2.0    git checkout 2f6cbc6 Library/Formula/postgresql.rb
9.1.5    git checkout 6b8d25f Library/Formula/postgresql.rb
9.1.4    git checkout c40c7bf Library/Formula/postgresql.rb
9.1.3    git checkout 05c7954 Library/Formula/postgresql.rb
9.1.2    git checkout dfcc838 Library/Formula/postgresql.rb
9.1.1    git checkout 4ef8fb0 Library/Formula/postgresql.rb
9.0.4    git checkout 2accac4 Library/Formula/postgresql.rb
9.0.3    git checkout b782d9d Library/Formula/postgresql.rb

As you can see, it advises against using it. Homebrew spits out all versions it can find with its internal heuristic and shows you a way to retrieve the old formulae. Let’s try it.

# First, go to the homebrew base directory
$ cd $( brew --prefix )
# Checkout some old formula
$ git checkout 6b8d25f Library/Formula/postgresql.rb
$ brew install postgresql
# … installing

Now that the older postgresql version is installed, we can re-install the latest formula in order to keep our repository clean:

$ git checkout -- Library/Formula/postgresql.rb

brew switch is your friend to change between the old and the new.

b) prehistoric times

For special needs, we may also try our own digging through the homebrew repo.

$ cd Library/Taps/homebrew/homebrew-core && git log -S'8.4.4' -- Formula/postgresql.rb

git log -S looks for all commits in which the string '8.4.4' was either added or removed in the file Library/Taps/homebrew/homebrew-core/Formula/postgresql.rb. We get two commits as a result.

commit 7dc7ccef9e1ab7d2fc351d7935c96a0e0b031552
Author: Aku Kotkavuo
Date:   Sun Sep 19 18:03:41 2010 +0300

    Update PostgreSQL to 9.0.0.

    Signed-off-by: Adam Vandenberg

commit fa992c6a82eebdc4cc36a0c0d2837f4c02f3f422
Author: David Höppner
Date:   Sun May 16 12:35:18 2010 +0200

    postgresql: update version to 8.4.4

Obviously, fa992c6a82eebdc4cc36a0c0d2837f4c02f3f422 is the commit we’re interested in. As this commit is pretty old, we’ll try to downgrade the complete homebrew installation (that way, the formula API is more or less guaranteed to be valid):

$ git checkout -b postgresql-8.4.4 fa992c6a82eebdc4cc36a0c0d2837f4c02f3f422
$ brew install postgresql
$ git checkout master
$ git branch -d postgresql-8.4.4

You may skip the last command to keep the reference in your git repository.

One note: When checking out the older commit, you temporarily downgrade your homebrew installation. So, you should be careful as some commands in homebrew might be different to the most recent version.

4) Manually write a formula

It’s not too hard and you may then upload it to your own repository. Used to be Homebrew-Versions, but that is now discontinued.

A.) Bonus: Pinning

If you want to keep a certain version of, say postgresql, around and stop it from being updated when you do the natural brew update; brew upgrade procedure, you can pin a formula:

$ brew pin postgresql

Pinned formulae are listed in /usr/local/Library/PinnedKegs/ and once you want to bring in the latest changes and updates, you can unpin it again:

$ brew unpin postgresql

Simple Workflow

Now that Homebrew/versions has been deprecated, Homebrew/core supports a few versions of formulae with a new naming format.

To install a specific version, e.g. postgresql 9.5 you simply run:

$ brew install postgresql@9.5

To list the available versions run a search with @:

$ brew search postgresql@
==> Searching local taps...
postgresql@10.1 ✔     postgresql@9.4        postgresql@9.5        postgresql@9.6

⚠ This answer won't work anymore after December 2020:
brew switch got disabled in HomeBrew 2.7.0 (deprecated in 2.6.0)

For versions of Homebrew before 2.7:

There's now a much easier way to install an older version of a formula that you'd previously installed. Simply use

brew switch [formula] [version]

For instance, I alternate regularly between Node.js 0.4.12 and 0.6.5:

brew switch node 0.4.12
brew switch node 0.6.5

Since brew switch just changes the symlinks, it's very fast. See further documentation on the Homebrew Wiki under External Commands.

Update: 1/15/2015

• Find the commit history of the desired software and version. e.g. I need to switch from docker version 1.4.1 to 1.3.3: https://github.com/Homebrew/homebrew-core/commits/master/Formula/docker.rb
• View the file with this button:
• Click the Raw button:
• Copy the URL (docker.rb url in this example) from address bar
• brew install <url> (may have to brew unlink first, e.g. brew unlink docker)
• brew switch docker 1.3.3
• Switch back to docker 1.4.1 brew switch docker 1.4.1

From this gist

brew update
brew versions FORMULA
cd `brew --prefix`
git checkout HASH Library/Formula/FORMULA.rb  # use output of "brew versions"
brew install FORMULA
brew switch FORMULA VERSION
git checkout -- Library/Formula/FORMULA.rb    # reset formula

## Example: Using Subversion 1.6.17
#
# $ brew versions subversion
# 1.7.3    git checkout f8bf2f3 /usr/local/Library/Formula/subversion.rb
# 1.7.2    git checkout d89bf83 /usr/local/Library/Formula/subversion.rb
# 1.6.17   git checkout 6e2d550 /usr/local/Library/Formula/subversion.rb
# 1.6.16   git checkout 83ed494 /usr/local/Library/Formula/subversion.rb
# 1.6.15   git checkout 809a18a /usr/local/Library/Formula/subversion.rb
# 1.6.13   git checkout 7871a99 /usr/local/Library/Formula/subversion.rb
# 1.6.12   git checkout c99b3ac /usr/local/Library/Formula/subversion.rb
# 1.6.6    git checkout 8774131 /usr/local/Library/Formula/subversion.rb
# 1.6.5    git checkout a82e823 /usr/local/Library/Formula/subversion.rb
# 1.6.3    git checkout 6b6d369 /usr/local/Library/Formula/subversion.rb
# $ cd `brew --prefix`
# $ git checkout 6e2d550 /usr/local/Library/Formula/subversion.rb
# $ brew install subversion
# $ brew switch subversion 1.6.17
# $ git checkout -- Library/Formula/subversion.rb

Along the lines of @halfcube's suggestion, this works really well:

1. Find the library you're looking for at https://github.com/Homebrew/homebrew-core/tree/master/Formula
2. Click it: https://github.com/Homebrew/homebrew-core/blob/master/Formula/postgresql.rb
3. Click the "history" button to look at old commits: https://github.com/Homebrew/homebrew-core/commits/master/Formula/postgresql.rb
4. Click the one you want: "postgresql: update version to 8.4.4", https://github.com/Homebrew/homebrew-core/blob/8cf29889111b44fd797c01db3cf406b0b14e858c/Formula/postgresql.rb
5. Click the "raw" link: https://raw.githubusercontent.com/Homebrew/homebrew-core/8cf29889111b44fd797c01db3cf406b0b14e858c/Formula/postgresql.rb
6. Download the .rb file to any folder (in this case: postgresql.rb)
7. In that folder: brew install postgresql.rb

Solution

brew extract --version=8.4p1  openssh homebrew/cask
brew install openssh@8.4p1

The newest openssl@8.5p1 has bugs after I run brew upgrade, so I backed to the previous version successfully via the above way.

I've discovered a better alternative solution then the other complex solutions.

brew install https://raw.github.com/Homebrew/homebrew-versions/master/postgresql8.rb

This will download and install PostgreSQL 8.4.8

I found this solution by starting to follow the steps of searching the repo and a comment in the repo .

After a little research found that someone has a collection of rare formulars to brew up with.

If your looking for MySQL 5.1.x, give this a try.

brew install https://raw.github.com/Homebrew/homebrew-versions/master/mysql51.rb

UPDATE: This method is deprecated and no longer works.

This method results in error: Installation of mysql from a GitHub commit URL is unsupported! brew extract mysql to a stable tap on GitHub instead. (UsageError)

$ brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/c77882756a832ac1d87e7396c114158e5619016c/Formula/mysql.rb
Updating Homebrew...
==> Auto-updated Homebrew!
Updated 2 taps (homebrew/core and homebrew/cask).

...

Traceback (most recent call last):
    9: from /usr/local/Homebrew/Library/Homebrew/brew.rb:122:in `<main>'
    8: from /usr/local/Homebrew/Library/Homebrew/cmd/install.rb:132:in `install'
    7: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:302:in `parse'
    6: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:651:in `formulae'
    5: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:651:in `map'
    4: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:655:in `block in formulae'
    3: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:351:in `factory'
    2: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:138:in `get_formula'
    1: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:142:in `klass'
/usr/local/Homebrew/Library/Homebrew/formulary.rb:227:in `load_file': Invalid usage: Installation of mysql from a GitHub commit URL is unsupported! `brew extract mysql` to a stable tap on GitHub instead. (UsageError)
    12: from /usr/local/Homebrew/Library/Homebrew/brew.rb:155:in `<main>'
    11: from /usr/local/Homebrew/Library/Homebrew/brew.rb:157:in `rescue in <main>'
    10: from /usr/local/Homebrew/Library/Homebrew/help.rb:64:in `help'
     9: from /usr/local/Homebrew/Library/Homebrew/help.rb:83:in `command_help'
     8: from /usr/local/Homebrew/Library/Homebrew/help.rb:103:in `parser_help'
     7: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:302:in `parse'
     6: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:651:in `formulae'
     5: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:651:in `map'
     4: from /usr/local/Homebrew/Library/Homebrew/cli/parser.rb:655:in `block in formulae'
     3: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:351:in `factory'
     2: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:138:in `get_formula'
     1: from /usr/local/Homebrew/Library/Homebrew/formulary.rb:142:in `klass'
/usr/local/Homebrew/Library/Homebrew/formulary.rb:227:in `load_file': Invalid usage: Installation of mysql from a GitHub commit URL is unsupported! `brew extract mysql` to a stable tap on GitHub instead. (UsageError)

I tried to install with the recommended command, but it doesn't work in this particular instance of MySQL 5.7.10. You may have better luck with a more recent Formula.

$ brew extract --version=5.7.10 mysql homebrew/cask
==> Searching repository history
==> Writing formula for mysql from revision 0fa511b to:
/usr/local/Homebrew/Library/Taps/homebrew/homebrew-cask/Formula/mysql@5.7.10.rb

$ 

$ brew install /usr/local/Homebrew/Library/Taps/homebrew/homebrew-cask/Formula/mysql@5.7.10.rb
Updating Homebrew...
==> Auto-updated Homebrew!
Updated 1 tap (homebrew/core).
==> Updated Formulae
Updated 1 formula.
Error: undefined method `core_tap?' for nil:NilClass

Error: Failed to load cask: /usr/local/Homebrew/Library/Taps/homebrew/homebrew-cask/Formula/mysql@5.7.10.rb
Cask 'mysql@5.7.10' is unreadable: wrong constant name #<Class:0x00007f9b9498cad8>
Warning: Treating /usr/local/Homebrew/Library/Taps/homebrew/homebrew-cask/Formula/mysql@5.7.10.rb as a formula.
==> Installing mysql@5.7.10 from homebrew/cask
==> Downloading https://homebrew.bintray.com/bottles/cmake-3.19.4.big_sur.bottle.tar.gz
==> Downloading from https://d29vzk4ow07wi7.cloudfront.net/278f2ad1caf664019ff7b4a7fc5493999c06adf503637447af13a617d45cf484?response-content-disposition=attachment%3Bfilenam
######################################################################## 100.0%
==> Downloading https://downloads.sourceforge.net/project/boost/boost/1.59.0/boost_1_59_0.tar.bz2
==> Downloading from https://phoenixnap.dl.sourceforge.net/project/boost/boost/1.59.0/boost_1_59_0.tar.bz2
######################################################################## 100.0%
==> Downloading https://cdn.mysql.com/Downloads/MySQL-5.7/mysql-5.7.10.tar.gz

curl: (22) The requested URL returned error: 404 Not Found
Error: Failed to download resource "mysql@5.7.10"
Download failed: https://cdn.mysql.com/Downloads/MySQL-5.7/mysql-5.7.10.tar.gz

You could modify the Formula at the path above (written in ruby) to attempt to achieve your desired result (e.g., an installation of MySQL 5.7.10 on a recent macOS version).

You can use the strategy of identifying the formula and a particular commit in the history of the formula that matches the version of the package you'd like to install.

1. Go to https://github.com/Homebrew/homebrew-core

2. Press t on your keyboard to activate the file finder.

3. Identify a formula that looks most relevant, perhaps: Formula/mysql.rb, bringing you to a forumla file location: https://github.com/Homebrew/homebrew-core/blob/master/Formula/mysql.rb.

4. Look at the revision history by clicking on the History button, which is located at https://github.com/Homebrew/homebrew-core/commits/master/Formula/mysql.rb. If you're interested in MySQL 5.7.10, you might want to click the latest revision prior to 5.7.11, which navigates to a GitHub commit:

https://github.com/Homebrew/homebrew-core/commit/c77882756a832ac1d87e7396c114158e5619016c#Formula/mysql.rb

NOTE: You may have to view the commit history in your console per GitHub's suggestion if the commit history does not load in your browser. Replace the commit SHA above in the URL if you're interested in seeing that commit on GitHub. Alternatively, skip to step 7, below.

5. Click the "View" button to view the source for the mysql.rb file after the commit was applied.

6. Then click the "Raw" button to view the raw source.

7. Copy the URL. Alternatively, build the URL yourself with the mysql.rb file name to identify your formula and the particular version of that formula (identified by the commmit SHA in the URL below).

https://raw.githubusercontent.com/Homebrew/homebrew-core/c77882756a832ac1d87e7396c114158e5619016c/Formula/mysql.rb

8. Install it with $ brew install [URL from step 7]

    $ brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/c77882756a832ac1d87e7396c114158e5619016c/Formula/mysql.rb
   

Most of the other answers are obsolete by now. Unfortunately Homebrew still doesn’t have a builtin way of installing an outdated version, unless that version exists as a separate formula (e.g. python@2, postgresql@9.4 …).

Luckily, for other formulas there’s a much easier way than the convoluted mess that used to be necessary. Here are the full instructions:

1. Search for the correct version in the logs:

   brew log formula
   # Scroll down/up with j/k or the arrow keys
   # or use eg. /4\.4\.23 to search a specific version
   
   # This syntax only works on pre-2.0 Homebrew versions
   brew log --format=format:%H\ %s -F --grep=‹version› ‹formula›
   

   This will show a list of commit hashes. Take one that is appropriate (mostly it should be pretty obvious, and usually is the most recent (i.e. top) one.

2. Find the URL at which the formula resides in the upstream repository:

   brew info ‹formula› | grep ^From:
   

3. Fix the URL:

   1. Replace github.com with raw.githubusercontent.com
   2. Replace blob/master with the commit hash we found in the first step.

4. Install the desired version by replacing master in the previously found URL by the commit hash, e.g.:

   brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/‹hash›/Formula/‹formula›.rb
   

(The last step may necessitate running brew unlink ‹formula› before.)

If you have copied a commit hash you want to use, you can use something like this example to install that version, replacing the value and bash with your commit hash and your desired formula.

BREW_VERSION_SHA=32353d2286f850fd965e0a48bcf692b83a6e9a41
BREW_FORMULA_NAME=bash
brew info $BREW_FORMULA_NAME \
| sed -n \
    -e '/^From: /s///' \
    -e 's/github.com/raw.githubusercontent.com/' \
    -e 's%blob/%%' \
    -e "s/master/$BREW_VERSION_SHA/p" \
| xargs brew install

This example is installing bash 4.4.23 instead of bash 5, though if you performed a brew upgrade afterward then bash 5 would get installed over top, unless you first executed brew pin bash. Instead to make this smoother WITHOUT pinning, you should first install the latest with brew install bash, then brew unlink bash, then install the older version you want per the script above, and then use brew switch bash 4.4.23 to set up the symlinks to the older version. Now a brew upgrade shouldn't affect your version of Bash. You can brew switch bash to get a list of the versions available to switch to.

Alternative using a custom local-only tap

Another way of achieving the same goal appears to be:

brew tap-new username/repo-name
# extract with a version seems to run a grep under the hood
brew extract --version='4.4.23' bash username/repo-name
brew install bash@4.4.23
# Note this "fails" when trying to grab a bottle for the package and seems to have
# some odd doubling of the version in that output, but this isn't fatal.

This creates a formula@version in your custom tap that you can install per the above example. The downside is that you probably still need to brew unlink bash and then brew link bash@4.4.23 in order to use your specific version of Bash or any other formula.

Official method ( judging from the response to https://github.com/Homebrew/brew/issues/6028 )

Unfortunately Homebrew still doesn’t have an obvious builtin way of installing an older version.

Luckily, for most formulas there’s a much easier way than the convoluted mess that used to be necessary. Here are the full instructions using bash as an example:

brew tap-new $USER/local-tap
# extract with a version seems to run a `git log --grep` under the hood
brew extract --version=4.4.23 bash $USER/local-tap
# Install your new version from the tap
brew install bash@4.4.23
# Note this "fails" trying to grab a bottle for the package and seems to have
# some odd doubling of the version in that output, but this isn't fatal.

This creates the formula@version in your custom tap that you can install per the above example. An important note is that you probably need to brew unlink bash if you had previously installed the default/latest version of the formula and then brew link bash@4.4.23 in order to use your specific version of Bash (or any other formula where you have latest and an older version installed).

A potential downside to this method is you can't easily switch back and forth between the versions because according to brew it is a "different formula".

If you want to be able to use brew switch $FORMULA $VERSION you should use the next method.

Scripted Method (Recommended)

This example shows installing the older bash 4.4.23, a useful example since the bash formula currently installs bash 5.

• First install the latest version of the formula with brew install bash
• then brew unlink bash
• then install the older version you want per the snippets below
• finally use brew switch bash 4.4.23 to set up the symlinks to your version

If you performed a brew upgrade after installing an older version without installing the latest first, then the latest would get installed clobbering your older version, unless you first executed brew pin bash.

The steps here AVOID pinning because it is easy to forget about and you might pin to a version that becomes insecure in the future (see Shellshock/etc). With this setup a brew upgrade shouldn't affect your version of Bash and you can always run brew switch bash to get a list of the versions available to switch to.

Copy and paste and edit the export lines from the code snippet below to update with your desired version and formula name, then copy and paste the rest as-is and it will use those variables to do the magic.

# This search syntax works with newer Homebrew
export BREW_FORMULA_SEARCH_VERSION=4.4.23 BREW_FORMULA_NAME=bash
# This will print any/all commits that match the version and formula name
git -C $(brew --repo homebrew/core) log \
--format=format:%H\ %s -F --all-match \
--grep=$BREW_FORMULA_SEARCH_VERSION --grep=$BREW_FORMULA_NAME

When you are certain the version exists in the formula, you can use the below:

# Gets only the latest Git commit SHA for the script further down
export BREW_FORMULA_VERSION_SHA=$(git -C $(brew --repo homebrew/core) log \
 --format=format:%H\ %s -F --all-match \
--grep=$BREW_FORMULA_SEARCH_VERSION --grep=$BREW_FORMULA_NAME | \
head -1 | awk '{print $1}')

Once you have exported the commit hash you want to use, you can use this to install that version of the package.

brew info $BREW_FORMULA_NAME \
| sed -n \
    -e '/^From: /s///' \
    -e 's/github.com/raw.githubusercontent.com/' \
    -e 's%blob/%%' \
    -e "s/master/$BREW_FORMULA_VERSION_SHA/p" \
| xargs brew install

Follow the directions in the formula output to put it into your PATH or set it as your default shell.

Homebrew changed recently. Things that used to work do not work anymore. The easiest way I found to work (January 2021), was to:

• Find the .rb file for my software (first go to Formulas, find the one I need and then click "History"; for CMake, this is at https://github.com/Homebrew/homebrew-core/commits/master/Formula/cmake.rb)
  • Pick the desired version among the revisions, e.g. 3.18.4, click three dots in the top right corner of the .rb file diff (...) and then click Raw. Copy the URL.
• Unlink the old version brew unlink cmake
• Installing directly from the git URL does not work anymore (brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/2bf16397f163187ae5ac8be41ca7af25b5b2e2cc/Formula/cmake.rb will fail)
  • Instead, download it and install from a local file curl -O https://raw.githubusercontent.com/Homebrew/homebrew-core/2bf16397f163187ae5ac8be41ca7af25b5b2e2cc/Formula/cmake.rb && brew install ./cmake.rb

Voila! You can delete the downloaded .rb file now.

I just used Homebrew to go back to Maven 2.2.1 since the simple brew install maven installed Maven 3.0.3.

First you have to leave the maven dir there so

$ brew unlink maven

Use the brew tap command

$ brew tap homebrew/versions
Cloning into '/usr/local/Library/Taps/homebrew-versions'...
remote: Counting objects: 590, done.
remote: Compressing objects: 100% (265/265), done.
remote: Total 590 (delta 362), reused 549 (delta 325)
Receiving objects: 100% (590/590), 117.49 KiB | 79 KiB/s, done.
Resolving deltas: 100% (362/362), done.
Tapped 50 formula

Now you can install the maven2 formula:

$ brew install maven2
==> Downloading http://www.apache.org/dist/maven/maven-2/2.2.1/binaries/apache-maven-2.2.1-bin.tar.gz
######################################################################## 100.0%
/usr/local/Cellar/maven2/2.2.1: 10 files, 3.1M, built in 6 seconds

$ mvn --version
Apache Maven 2.2.1 (r801777; 2009-08-06 12:16:01-0700)
Java version: 1.6.0_37
Java home: /System/Library/Java/JavaVirtualMachines/1.6.0.jdk/Contents/Home
Default locale: en_US, platform encoding: MacRoman
OS name: "mac os x" version: "10.7.4" arch: "x86_64" Family: "mac" 

Edit: You can also just brew switch maven 2.2.1 to switch to a different version.

Edit: The Apache Maven project reorganized their repo. Updated this answer to account for this change.

Upgraded Postgres by accident?

My case:

• postgresql was upgraded from 11 to 12 accidentally (after running brew upgrade without arguments)
• I want to keep Postgres 11.

Solution:

1. Stop the DB:

brew services stop postgresql

2. Install Postgres 11:

brew install postgresql@11

3. Enable it:

brew link postgresql@11 --force

4. (Optional) Rename DB data directory from postgres to postgres@11:

cd /usr/local/var
ls -lh
mv postgresql@11 postgresql@11-fresh-backup
mv postgres postgresql@11

5. Start the DB:

brew services start postgresql@11

If you have any errors, check /usr/local/var/log/postgresql@11.log (notice the @11).

Based on the workflow described by @tschundeee and @Debilski’s update 1, I automated the procedure and added cleanup in this script.

Download it, put it in your path and brewv <formula_name> <wanted_version>. For the specific OP, it would be:

cd path/to/downloaded/script/
./brewv postgresql 8.4.4

:)

None of the other answers cover this adequately for 2022, so I'm adding these instructions that are adapted from a Homebrew maintainer's answer for a similar question for installing a specific Cask version: https://stackoverflow.com/a/62765875/6310633

Uninstall your formula

brew uninstall <formula>

Switch over to your clone of the homebrew-core repo and reset to a commit containing the version you want.

cd "$(brew --prefix)/Library/Taps/homebrew/homebrew-core/Formula"
git log <formula>.rb # examine recent commits for <formula>
git reset --hard <commit-sha> # reset clone to last known-good commit for <formula>

Checkout a new branch for your version so brew won't autorefresh master after each command, install your formula, and pin it.

git checkout -b <formula>-downgrade-<version>
brew install <formula>
brew pin <formula>

Clean up

git checkout master
brew update

When you're ready to upgrade your formula, you can brew unpin <formula> and upgrade as usual.

An updated answer since that adds to what @lance-pollard already posted as working answer.

How to Install specific version of a Formula (formula used in this example is terraform):

1. Find your formula file, e.g: https://github.com/Homebrew/homebrew-core/blob/master/Formula/terraform.rb
2. Get the commit version from github’s history with https://github.com/Homebrew/homebrew-core/commits/master/Formula/terraform.rb or git log master -- Formula/terraform.rb if you have cloned the repo locally.
3. Get the raw git URL with the commit version of your formula: If the formula link in github.com is https://github.com/Homebrew/homebrew-core/blob/e4ca4d2c41d4c1412994f9f1cb14993be5b2c59a/Formula/terraform.rb, your raw URL will be: https://raw.githubusercontent.com/Homebrew/homebrew-core/e4ca4d2c41d4c1412994f9f1cb14993be5b2c59a/Formula/terraform.rb
4. Install it with: brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/e4ca4d2c41d4c1412994f9f1cb14993be5b2c59a/Formula/terraform.rb

The other answers here are great, but if you need to install an older version of the package and ensure that the package name is modified, you'll need a different approach. This is important when using scripts (in my case, PHP build scripts) which use brew --prefix package_name to determine what directory to use for compilation.

If you are using brew extract a version is added to the end of the package name which will break the brew --prefix lookup.

Here's how to install an older package version while maintaining the original package name:

# uninstall the newer version of the package that you accidentally installed
brew uninstall --ignore-dependencies icu4c

# `extract` the version you'd like to install into a custom tap
brew tap-new $USER/local-tap
brew extract --version=68.2 icu4c $USER/local-tap

# jump into the new tap you created
cd $(brew --repository $USER/local-tap)/Formula

# rename the formula
mv icu4c@68.2.rb icu4c.rb

# change the name of the formula by removing "AT682" from the `class` definition
# the exact text you'll need to remove will be different
# depending on the version you extracted
nano icu4c.rb

# then, install this specific formula directly
brew install $(brew --repository $USER/local-tap)/Formula/icu4c.rb

I wrote more about this here.

On the newest version of homebrew (0.9.5 as of this writing) there will be a specific recipe for the version of the homebrew keg you want to install. Example:

$ brew search mongodb
mongodb    mongodb24  mongodb26

Then just do brew install mongodb26 like normal.

In the case that you had already installed the latest version, make sure to unlink the latest version and link the desired version: brew unlink mongodb && brew link mongodb26.

The problem with homebrew/versions is that someone has to have that specific version of software listed in the repository for you to be able to use it. Also, since brew versions is no longer supported, another solution is required. For solutions that indicate using brew switch, this will only work if you haven't done a brew cleanup since the version needs to exist on your computer.

I had a problem with wanting to install a specific older version of docker-machine which wasn't listed in homebrew/versions. I solved this using the below, which should also work for any brew installed software. The example below will use docker-machine as the package I want to downgrade from version 0.5.0 to 0.4.1.

1. Go to your homebrew Formula directory.
   You can determine this by running brew info [any package name]. For example, brew info docker-machine gives me a line that shows me a path - /usr/local/Cellar/docker-machine/0.5.0. This tells me that on my machine, homebrew is installed at /usr/localand my Formula directory is located by default at /usr/local/Library/Formula

2. Locate the specific formula file (.rb) for your package. Since I want to downgrade docker-machine, I can see a docker-machine.rb file.

3. Get the version history for this formula file . Enter git log docker-machine.rb. This will list out the complete commit history for this file. You will see output like this:

    ...more 

    commit 20c7abc13d2edd67c8c1d30c407bd5e31229cacc
    Author: BrewTestBot 
    Date:   Thu Nov 5 16:14:18 2015 +0000

        docker-machine: update 0.5.0 bottle.

    commit 8f615708184884e501bf5c16482c95eff6aea637
    Author: Vincent Lesierse 
    Date:   Tue Oct 27 22:25:30 2015 +0100

        docker-machine 0.5.0

        Updated docker-machine to 0.5.0

        Closes #45403.

        Signed-off-by: Dominyk Tiller 

    commit 5970e1af9b13dcbeffd281ae57c9ab90316ba423
    Author: BrewTestBot 
    Date:   Mon Sep 21 14:04:04 2015 +0100

        docker-machine: update 0.4.1 bottle.

    commit 18fcbd36d22fa0c19406d699308fafb44e4c8dcd
    Author: BrewTestBot 
    Date:   Sun Aug 16 09:05:56 2015 +0100

        docker-machine: update 0.4.1 bottle.

    ...more

The tricky part is to find the latest commit for the specific version you want. In the above, I can tell the latest 0.4.1 version was committed with this commit tag : commit 5970e1af9b13dcbeffd281ae57c9ab90316ba423. The commits above this point start using version 0.5.0 (git log entries are listed from latest to earliest date).

4. Get a previous version of the formula file. Using the commit tag from step #3 (you can use the first 6 chars), you can get an older version of the formula file using the following:

   git checkout 5970e1 docker-machine.rb

5. Uninstall your current package version. Just run the normal brew commands to uninstall the current version of your package.
   Ex. brew uninstall docker-machine

6. Install the older package version Now, you can just run the normal brew install command and it will install the formula that you have checkout out. Ex. brew install docker-machine

You may need to re-link by using the brew link docker-machine if necessary.

If at any time you want to revert back to the latest version of a specific package, go into the Formula directory and issue the following commands on your formula file (.rb)

git reset HEAD docker-machine.rb
git checkout -- docker-machine.rb

Then you can brew uninstall docker-machine and brew install docker-machine to get the latest version and keep it that way going forward.

Edit: 2021, this answer is no longer functional due to the github install being deprecated. (Thanks Tim Smith for update).

Install an old brew package version (Flyway 4.2.0 example)

Find your local homebrew git dir or clone Homebrew/homebrew-core locally

cd /usr/local/Homebrew/Library/Taps/homebrew/homebrew-core/

OR

git clone git@github.com:Homebrew/homebrew-core.git

List all available versions

git log master -- Formula/flyway.rb

Copy the commit ID for the version you want and install it directly

brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/793abfa325531415184e1549836c982b39e89299/Formula/flyway.rb

I've tried most of the solutions here and they are outdated. I had to combine some ideas from here with my own work. As a result I've created a script to help me do the heavy lifting which you can find here

Usage:

brewv.sh formula_name desired_version

Currently the old ways of installing specific formula versions have been deprecated. So it seems like we have to use brew edit [formula]. E.g. say we want to install an the 62.1 version of icu4c (needed e.g. for postgresql 10.5). Then you'd have to

> brew edit icu4c
# drops you to editor

Here you'd have to alter the url, version and sha256 (perhaps also mirror) to the corresponding 62.1 strings.

url "https://ssl.icu-project.org/files/icu4c/62.1/icu4c-62_1-src.tgz"
mirror "https://github.com/unicode-org/icu/releases/download/release-62-1/icu4c-62_1-src.tgz"
version "62.1"
sha256 "3dd9868d666350dda66a6e305eecde9d479fb70b30d5b55d78a1deffb97d5aa3"

then run brew reinstall icu4c to finally download the 62.1 version.

it could be done very easy for last version of brew.

brew tap homebrew/versions
brew install subversion17 # for svn 1.7 branch instead of last available
brew install postgresql8  # for postgresql 8 (which you ask)

None of these really worked for my case (Python), so I'll add my 2 cents:

cd `brew --prefix`
git log Library/Formula/python.rb

Output looks like this:

commit 9ff2d8ca791ed1bd149fb8be063db0ed6a67a6de
Author: Dominyk Tiller <dominyktiller@gmail.com>
Date:   Thu Jun 30 17:42:18 2016 +0100

    python: clarify pour_bottle reason

commit cb3b29b824a264895434214e191d0d7ef4d51c85
Author: BrewTestBot <brew-test-bot@googlegroups.com>
Date:   Wed Jun 29 14:18:40 2016 +0100

    python: update 2.7.12 bottle.

commit 45bb1e220341894bbb7de6fd3f6df20987dc14f0
Author: Rakesh <rakkesh@users.noreply.github.com>
Date:   Wed Jun 29 10:02:26 2016 +0530

    python 2.7.12

    Closes #2452.

    Signed-off-by: Tim D. Smith <git@tim-smith.us>

commit cf5da0547cd261f79d69e7ff62fdfbd2c2d646e9
Author: BrewTestBot <brew-test-bot@googlegroups.com>
Date:   Fri Jun 17 20:14:36 2016 +0100

    python: update 2.7.11 bottle.

...

I want version 2.7.11 so my hash is cf5da0547cd261f79d69e7ff62fdfbd2c2d646e9 (or cf5da05 for short). Next, I check out that version and install the formula python:

git checkout cf5da05
brew install python

Finally, clean up:

git checkout master

If you can't find your version with brew search <formula>, you can also try going over the commit logs for your formula to find the version you want:

here is an example for installing an older version of nginx via brew:

• ngxnx formula commit log

• see nginx: update 1.6.3 bottle eba75b9a1a474b9fc4df30bd0a32637fa31ec049

From there, we can install 1.6.3 with the sha and raw git url:

brew install https://raw.githubusercontent.com/Homebrew/homebrew/eba75b9a1a474b9fc4df30bd0a32637fa31ec049/Library/Formula/nginx.rb

Here my simple answer for it - was really annoyed that there is no built in solution for that so I've built my own lazy "script". Feel free to contribute 😃👍🏻

# Please define variables
packageName=<packageName>
packageVersion=<packageVersion>

# Create a new tab
brew tap-new local/$packageName

# Extract into local tap
brew extract --version=$packageVersion $packageName local/$packageName

# Verify packages is present
brew search $packageName@

# Run brew install@version as usual
brew install local/$packageName/$packageName@$packageVersion

https://gist.github.com/ArgonQQ/cff4834dab6b254cc2140bb1454b47ef

I created a tool to ease the process prescribed in this answer.

To find a package pkg with version a.b.c, run:

$ brew-install-specific pkg@a.b.c

This will list commits on the pkg homebrew formula that mention the given version along with their GitHub urls.

Matching versions:
1. pkg: update a.b.c bottle.
   https://github.com/Homebrew/homebrew-core/commit/<COMMIT-SHA>
2. pkg: release a.b.c-beta
   https://github.com/Homebrew/homebrew-core/commit/<COMMIT-SHA>
3. pkg a.b.c
   https://github.com/Homebrew/homebrew-core/commit/<COMMIT-SHA>

Select index: 

Verify the commit from the given URL, and enter the index of the selected commit.

Select index: 2
Run:
  brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/<COMMIT-SHA>/Formula/pkg.rb

Copy and run the given command to install.

Closest to @Lance's answer but that didn't work for me as is, in 2023, using M1 macOS 13 and trying to install specific version of opencv@4.

Bottom-line is: you should override the content of your local opencv.rb file with that of the remote opencv.rb file found in brew's GitHub repo, that corresponds to the version of opencv you want to install.

Essentially, we want to update the url and sha256 in the .rb file for the package. But sha256 were not available from the opencv Releases Github page and creating sha256 locally throws a checksum error for me. But getting them from the .rb file from the commit history resolves this issue.

Breakdown: in 5 simple steps

1. Uninstall the package first: brew uninstall opencv@4

2. Find the .rb file for the correct version of the package you want to install

   1. Search under Homebrew > Homebrew-core > Formula on Github

   2. In the history of the opencv.rb file: https://github.com/Homebrew/homebrew-core/commits/master/Formula/opencv.rb

      • Select the commit you want corresponding to the desired version, say opencv: update 4.6.0_1 bottle. and View file.
      • Copy the contents of / Download the file

3. Open the .rb file on your system: brew edit opencv@4

4. Replace the contents of this file with the file you downloaded from Github

5. Install the package again using the .rb file path: brew install /opt/homebrew/Library/Taps/homebrew/homebrew-core/Formula/opencv.rb

This worked perfectly for me, whereas, @Lance's answer using brew install gave an Error: Your Command Line Tools (CLT) does not support macOS 13.

None of the other answers worked for me either.

Update on the Library/Formula/postgresql.rb line 8 to

http://ftp2.uk.postgresql.org/sites/ftp.postgresql.org/source/v8.4.6/postgresql-8.4.6.tar.bz2

And MD5 on line 9 to

fcc3daaf2292fa6bf1185ec45e512db6

Save and exit.

brew install postgres
initdb /usr/local/var/postgres

Now in this stage you might face the postgresql could not create shared memory segment error, to work around that update the /etc/sysctl.conf like this:

kern.sysv.shmall=65536
kern.sysv.shmmax=16777216

Try initdb /usr/local/var/postgres again, and it should run smooth.

To run postgresql on start

launchctl load -w /usr/local/Cellar/postgresql/8.4.6/org.postgresql.postgres.plist

Hope that helps :)

I just copied an older release of elasticsearch into the /usr/local/Cellar/elasticsearch directory.

$ mkdir /usr/local/Cellar/elasticsearch/5.4.3/bin
$ cp elasticsearch /usr/local/Cellar/elasticsearch/5.4.3/bin
$ brew switch elasticsearch 5.4.3

That's it. Maybe it's useful for anyone.