事前に

brewを最新にしておきましょう

brew update
brew upgrade

tapコマンドを使って、リポジトリを追加します

brew tap homebrew/dupes
brew tap homebrew/versions
brew tap homebrew/homebrew-php

インストール

> 現在インストールされているphpのバージョンはunlinkします

11:05:19 ~/  $ brew unlink php56
Unlinking /usr/local/Cellar/php56/5.6.29_5... 17 symlinks removed

unlinkしないと、以下のようなエラーが出ます

$ brew install php71
==> Installing php71 from homebrew/php
Error: Cannot install homebrew/php/php71 because conflicting formulae are installed.

  php56: because different php versions install the same binaries.

Please `brew unlink php56` before continuing.

Unlinking removes a formula's symlinks from /usr/local. You can
link the formula again after the install finishes. You can --force this
install, but the build may fail or cause obscure side-effects in the
resulting software.

> php71をbrew installします


 $ brew install php71
==> Installing php71 from homebrew/php
==> Downloading https://homebrew.bintray.com/bottles-php/php71-7.1.0_11.el_capitan.bottle.tar.gz
######################################################################## 100.0%
==> Pouring php71-7.1.0_11.el_capitan.bottle.tar.gz
==> Caveats
The php.ini file can be found in:
    /usr/local/etc/php/7.1/php.ini

✩✩✩✩ Extensions ✩✩✩✩

If you are having issues with custom extension compiling, ensure that
you are using the brew version, by placing /usr/local/bin before /usr/sbin in your PATH:

      PATH="/usr/local/bin:$PATH"

PHP71 Extensions will always be compiled against this PHP. Please install them
using --without-homebrew-php to enable compiling against system PHP.

✩✩✩✩ PHP CLI ✩✩✩✩

If you wish to swap the PHP you use on the command line, you should add the following to ~/.bashrc,
~/.zshrc, ~/.profile or your shell's equivalent configuration file:

      export PATH="$(brew --prefix homebrew/php/php71)/bin:$PATH"

✩✩✩✩ FPM ✩✩✩✩

To launch php-fpm on startup:
    mkdir -p ~/Library/LaunchAgents
    cp /usr/local/opt/php71/homebrew.mxcl.php71.plist ~/Library/LaunchAgents/
    launchctl load -w ~/Library/LaunchAgents/homebrew.mxcl.php71.plist

The control script is located at /usr/local/opt/php71/sbin/php71-fpm

OS X 10.8 and newer come with php-fpm pre-installed, to ensure you are using the brew version you need to make sure /usr/local/sbin is before /usr/sbin in your PATH:

  PATH="/usr/local/sbin:$PATH"

You may also need to edit the plist to use the correct "UserName".

Please note that the plist was called 'homebrew-php.josegonzalez.php71.plist' in old versions
of this formula.

With the release of macOS Sierra the Apache module is now not built by default. If you want to build it on your system
you have to install php with the --with-httpd24 option. See  brew options php71  for more details.

To have launchd start homebrew/php/php71 now and restart at login:
  brew services start homebrew/php/php71
==> Summary
🍺  /usr/local/Cellar/php71/7.1.0_11: 342 files, 39.7M

確認

 $ php --version
PHP 7.1.0 (cli) (built: Dec  2 2016 03:30:24) ( NTS )
Copyright (c) 1997-2016 The PHP Group
Zend Engine v3.1.0-dev, Copyright (c) 1998-2016 Zend Technologies

参考

Install PHP7.1 on OSX with homebrew — Jack Skinner — Ramblings of a programmer