Google App Engine is a PaaS and cannot run any Java Server application that you have written.
So, you will have to make sure that you understand the App Engine platform and write applications using various services that are provided as part of the platform.
To get started, check the following: https://developers.google.com/appengine/docs/java/gettingstarted/introduction
Google also has an offering called Compute Engine, that provides you with Linux VMs hosted on the Google infrastructure.
So if you are looking at VMs, where you want to host your application, you could look at that. You definitely have more flexbility with the Compute Engine but you have to deal with configuration, settings things up and more Administrative stuff.
Compute Engine is not free whereas App Engine comes with a generous free quota.