Here is a quick and dirty hack to keep your assembly version numbers synchronized with the TeamCity build number.
Set your build number format in your Build Conguration to a combination of the following configuration parameters.
Build number format = %MAJOR%.%MINOR%.{0}.%REVISION%

Create a new Command Line build runner and feed it with the following PowerShell script and reorder the build steps so that the PowerShell script runs before any MSBuild runners.
Command executable = powershell.exe
Command parameters = "(gc AssemblyInfo.cs) |
ForEach-Object
{ (($_
-replace \"^(.*AssemblyVersion.{1}).*(.{2})$\", '$1\"%ASSEMBLYVERSION%\"$2')
-replace \"^(.*AssemblyFileVersion.{1}).*(.{2})$\", '$1\"%ASSEMBLYFILEVERSION%\"$2')
-replace \"^(.*AssemblyInformationalVersion.{1}).*(.{2})$\", '$1\"%ASSEMBLYINFORMATIONALVERSION%\"$2'
} | sc AssemblyInfo.cs"

Finally, create the following Configuration Parameters in Properties and Environment Variables and Build your project.
%ASSEMBLYFILEVERSION% = %env.BUILD_NUMBER%
%ASSEMBLYINFORMATIONALVERSION% = "%MAJOR%.%MINOR% %REVISIONSTRING% %env.BUILD_VCS_NUMBER_Hg_test%"
%ASSEMBLYVERSION% = %MAJOR%.%MINOR%.0.0
%MAJOR% = 0
%MINOR% = 3
%REVISION% = 203
%REVISIONSTRING% = "Beta II"

And viola! Here is what your checked-out copy of the AssemblyInfo should look like before building your assemblies.
[assembly: AssemblyVersion("0.3.0.0")]
[assembly: AssemblyFileVersion("0.3.1.203")]
[assembly: AssemblyInformationalVersion("0.3 Beta II 5558fffc26f6")]
Please note that, in this example, I’m using Mercurial as my VCS so 5558fffc26f6 is the Mercurial changeset hash. Your AssemblyInformationalVersion would look similar when Git is used as your VCS. So the %REVISION% number above is just a numerical representation of the value of %REVISIONSTRING%, and for obvious reasons, not the incremental revision number from the local DVCS node.
For Subversion and other centralized version control systems, you could set your %REVISION% number to the incremental revision number since the revision numbers are identical across each machine.
%REVISION% = %env.BUILD_VCS_NUMBER_SVN_test%