If you're receiving a missing file exception when trying to build an SSDT database project on TeamCity, you may have to copy a dependency to your build machine.
\[10:00:08\]\[SqlBuildTask\] C:\\Program Files (x86)\\MSBuild\\Microsoft\\VisualStudio\\v10.0\\SSDT\\Microsoft.Data.Tools.Schema.SqlTasks.targets(494, 5): error SQL72027: File "C:\\Extensions\\Microsoft\\SQLDB\\Extensions\\SqlServer\\Azure\\SqlSchemas\\master.dacpac" does not exist.
This results from adding a database reference to your SSDT database project to the master or msdb databases. Those files are stored in a local folder, and are not included in your project. As such, they're missing from the TeamCity server.
To fix this issue, copy files from C:\Program Files (x86)\Microsoft Visual Studio 10.0\Common7\IDE\Extensions\Microsoft\SQLDB\Extensions\SqlServer\110\SQLSchemas to your TeamCity server:
I had to create the path on the TeamCity server (C:\Extensions didn't exist at all):
And then dropped the files in there. Started a rebuild and everything worked again.
Note: paths may vary based on your system, versions installed, or configuration.