Place this file within .ebextensions/ which should be located in the root folder on the same level as your /app and /vendor folders.

myapp.config

commands:
   01updateComposer:
      command: export COMPOSER_HOME=/root && /usr/bin/composer.phar self-update
 
option_settings:
   - namespace: aws:elasticbeanstalk:application:environment
     option_name: COMPOSER_HOME
     value: /root
 
files:
  "/var/app/composer.json":
      mode: "000744"
      content:
         {
            "require": {
               "aws/aws-sdk-php": "*"
             }
          }
 
container_commands:
   "1-install-composer":
      command: "cd /var/app; curl -s http://getcomposer.org/installer | php"
   "2-install-dependencies":
      command: "cd /var/app; php composer.phar install"
   "3-cleanup-composer":
      command: "rm -Rf /var/app/composer.*"

For a prod server you might want to add --optimize-autoloader as an argument to the composer install in the 2-install-dependencies coomand.

Reference: https://getcomposer.org/doc/03-cli.md
--optimize-autoloader (-o): Convert PSR-0/4 autoloading to classmap to get a faster autoloader. This is recommended especially for production, but can take a bit of time to run so it is currently not done by default.