1. Prerequisites
Shell access to a running macOS
PHP 5.3 or higher version must be installed

2. Install Composer on macOS
Download composer binary file from getcomposer.org website by running the following command. It will create a composer.phar file in the current directory.

curl -sS https://getcomposer.org/installer | php

Now, copy this composer.phar file under bin directory to make available anywhere in the system. Also, set the execute permission on file. I have changed the filename from composer.phar to composer for the easy use.

mv composer.phar /usr/local/bin/composer
chmod +x /usr/local/bin/composer

Run composer command on the command prompt. This will provide you composer version details along with options available with composer command.

composer 

   ______
  / ____/___  ____ ___  ____  ____  ________  _____
 / /   / __ \/ __ `__ \/ __ \/ __ \/ ___/ _ \/ ___/
/ /___/ /_/ / / / / / / /_/ / /_/ (__  )  __/ /
\____/\____/_/ /_/ /_/ .___/\____/____/\___/_/
                    /_/
Composer version 1.9.0 2019-08-02 20:55:32

Usage:
  command [options] [arguments]

Options:
  -h, --help                     Display this help message
  -q, --quiet                    Do not output any message
  -V, --version                  Display this application version
      --ansi                     Force ANSI output
      --no-ansi                  Disable ANSI output

3. Upgrade PHP Composer

The PHP composer provides a command-line option (self-update) to upgrade itself. You can simply run below command from the terminal to upgrade compose on your macOS.

sudo composer self-update