Steps:

1. Visit Developers Console.
2. In your project: Compute -> App Engine -> Settings.
3. On the tab labelled CUSTOM DOMAINS, you can verify your domain and assign it and/or its subdomains to your GAE project.
4. Add the DNS settings provided by Google into the DNS server of your domain provider.

Notes:

1. Only HTTP is supported, HTTPS is not.
2. It will not work if you only modify the DNS record without actually assigning the custom domain in the Developer Console.