Thanks to Yole's direction, I've set this up now.
The steps if anyone is interested are below:
- Install Gradle on the build agent server. I took the gradle-2.3.bin from http://gradle.org/downloads and copied to C:\gradle-2.3
- Set the environment variable GRADLE_HOME = C:\gradle-2.3
- Install Android Studio on the build agent server. This should also install the Android SDK
- Set the environment variable ANDROID_HOME = C:\Users\%Current User%\AppData\Local\Android\sdk
- Restart the TeamCity agent server
- Setup your build configuration with the Gradle runner, setting Gradle tasks to 'clean build' and setting the Gradle Home path. Set working directory to the project directory for your Android project
Run the build!