You’re looking for:
brew install git bash-completion
As warpc’s comment states, you’ll need to add the following to your ~/.bash_profile to get homebrew’s bash-completion working:
if [ -f $(brew --prefix)/etc/bash_completion ]; then
. $(brew --prefix)/etc/bash_completion
fi
The above is mentioned in the caveats when you install the bash-completion formula.
Note: if you are using Bash v4 or later (via brew install bash) then you’re going to want to use brew install bash-completion@2, to enable tab completion add the following to ~/.bash_profile as described in the caveats:
export BASH_COMPLETION_COMPAT_DIR="/usr/local/etc/bash_completion.d"
[[ -r "/usr/local/etc/profile.d/bash_completion.sh" ]] && . "/usr/local/etc/profile.d/bash_completion.sh"
The additional export is necessary for git, docker, youtube-dl, and other completions which may be included in the $(brew --prefix)/etc/bash_completion.d/ directory.