Git completion not working in zsh on OS X Yosemite with Homebrew

I just stumbled upon the answer!

In my case I was missing a few important pieces in my .zshrc file. But first a little background:

What I'm trying to do is setup the "zsh Completion System". It comes with a lot of commands all named something with comp*. I tried to run these a few times but in many cases zsh would just tell me it didn't know them. So aparently you have to autoload them, among other things.

This is what I did:

I added the following lines to my .zshrc file:

autoload -U compinit && compinit
zmodload -i zsh/complist

Then I opened a new terminal and ran:

rm -f ~/.zcompdump; compinit

Then I opened a new terminal and now git <tab> worked as expected :)

If you are setting up a custom $fpath in your .zshrc file I would recommend adding these lines after you've modified the $fpath (though I don't know if it makes a difference).

Since macOS Catalina,...
Apple has switched from bash to zsh as their default shell.

Now the only brew command you need to activate zsh-completion (which includes git completion) is this...

brew install zsh-completion

Then add this block to your ~/.zshrc file (which you may have to create first):

if type brew &>/dev/null; then
  FPATH=$(brew --prefix)/share/zsh-completions:$FPATH

  autoload -Uz compinit
  compinit
fi

See my answer on AskDifferent for more details:
https://apple.stackexchange.com/a/392382/77452