I cannot for the life of me find any reference on the internet for how to setup TeamCity to build Android Studio projects.
I\'ve found links to IntelliJ Idea and TeamCi
Thanks to Yole's direction, I've set this up now.
The steps if anyone is interested are below:
Run the build!
There is nothing specific about building an Android Studio project on TeamCity. It's just a Gradle project, and you need to configure it as such.