For FxCop 14.0 / VS2015 see this answer
Run FxCop 12.0 without installing Visual Studio 2013
Okay, i've invested 6 hours and now it's working.
I've added all necessary executables, dlls and msbuild targets to source control.
These are the files that i had to add to source control:
(Please consider that this might violate some license agreements)
(source control)\dev\tools\FxCop
│
├[amd64]
│   │
│   └msdia120.dll
├[Engines]
│   │
│   ├IntrospectionAnalysisEngine.dll
│   └PhoenixAnalysisEngine.dll
├[Msbuild]
│   │
│   ├fxcoptask.dll
│   ├Microsoft.CodeAnalysis.Targets
│   ├Microsoft.VisualStudio.CodeAnalysis.dll
│   └Microsoft.VisualStudio.CodeAnalysis.Sdk.dll
├[Repository]
│   │
│   ├[Compatibility]
│   │   │
│   │   ├Desktop2.0.xml
│   │   ├Desktop2.0SP1.xml
│   │   ├Desktop2.0SP2.xml
│   │   ├Desktop3.0.xml
│   │   ├Desktop3.0SP1.xml
│   │   ├Desktop3.0SP2.xml
│   │   ├Desktop3.5.xml
│   │   └Desktop3.5SP1.xml
│   └system32.bin
├[Rules]
│   │
│   ├DataflowRules.dll
│   ├DesignRules.dll
│   ├GlobalizationRules.dll
│   ├InteroperabilityRules.dll
│   ├MaintainabilityRules.dll
│   ├MobilityRules.dll
│   ├NamingRules.dll
│   ├PerformanceRules.dll
│   ├PortabilityRules.dll
│   ├ReliabilityRules.dll
│   ├SecurityRules.dll
│   ├SecurityTransparencyRules.dll
│   └UsageRules.dll
├[Xml]
│   │
│   ├CodeAnalysisReport.xsl
│   ├FxCopReport.xsl
│   └VSConsoleOutput.xsl
├Architecture-msil.dll
├CodeAnalysis.dll
├CustomDictionary.xml
├FxCopCmd.exe
├FxCopCmd.exe.config
├FxCopCommon.dll
├FxCopSdk.dll
├Microsoft.Cci.dll
├Microsoft.VisualStudio.CodeAnalysis.Common.dll
├Microsoft.VisualStudio.CodeAnalysis.DataflowModels.dll
├Microsoft.VisualStudio.CodeAnalysis.dll
├Microsoft.VisualStudio.CodeAnalysis.Interop.dll
├Microsoft.VisualStudio.CodeAnalysis.Phoenix.dll
├Microsoft.VisualStudio.CodeAnalysis.Phoenix.xml
├msdia120.dll
├mssp7en.dll
├mssp7en.lex
├phx.dll
└Runtime-vccrt-win-msil.dll
Copy them as follows:
- entire FxCop installation folder contents from - %programfiles(x86)%\Microsoft Visual Studio 12.0\Team Tools\Static Analysis Tools\FxCop
 
- from Visual Studio 2013 C++ redist, or any other place: 
(also see legal information) copy msdia120 x86 and x64 to: - msdia120.dll (874 KiB) - amd64\msdia120.dll (1.07 MiB) 
- from the Global Assembly Cache (- C:\Windows\Microsoft.NET\assembly\GAC_MSIL\_NameOfTheAssembly_\) of a computer where VS2013 is installed, copy the following DLLs to:
(Make sure the DLLs are version 12.0 !)
 - Msbuild\Microsoft.VisualStudio.CodeAnalysis.dll - Msbuild\Microsoft.VisualStudio.CodeAnalysis.Sdk.dll 
- All files from - %programfiles(x86)%\MSBuild\Microsoft\VisualStudio\v12.0\CodeAnalysisto
 - Msbuild\fxcoptask.dll - Msbuild\Microsoft.CodeAnalysis.Targets 
(Furthermore you need the appropriate Windows (7.1 / 8.1) SDK for building the .net 4.0 / 4.5 application installed on the build agent)
Additionally we had to adjust the project msbuild file as follows:
<!--Must import code analysis target before importing csharp targets, so that the correct code analysis targets gets imported. -->
<Import Project="$(ProjectBuildScriptDir)Custom.CodeAnalysis.targets"/>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets"/>
And this is what our Custom.CodeAnalysis.targets contains:
    
    
  <PropertyGroup>
    <!-- Code analysis settings. -->
    <CodeAnalysisCulture>en-US</CodeAnalysisCulture>
    <!-- change this so it points to your ruleset or remove it entirely -->
    <CodeAnalysisRuleSet>$(SourcesDir)Custom.ruleset</CodeAnalysisRuleSet>
    <!-- this must refer to the source control directory where you copied FxCopCommand.exe (and the rest of the FxCop files and directories...) to -->
    <CodeAnalysisPath>$(ToolsDir)FxCop\</CodeAnalysisPath>
    <!-- this must refer to the source control directory where you copied fxcoptask.dll, Microsoft.CodeAnalysis.Targets, Microsoft.VisualStudio.CodeaAnalysis.dll and Microsoft.VisualStudio.CodeaAnalysis.Sdk.dll to -->
    <CodeAnalysisTargets>$(CodeAnalysisPath)Msbuild\Microsoft.CodeAnalysis.Targets</CodeAnalysisTargets>
  </PropertyGroup>
  <!-- configure this according to your wishes -->
  <PropertyGroup Condition="'$(Configuration)' == 'Release'">
    <CodeAnalysisTreatWarningsAsErrors>false</CodeAnalysisTreatWarningsAsErrors>
    <RunCodeAnalysis>true</RunCodeAnalysis>
  </PropertyGroup>
  <!-- Report code analysis results to TeamCity -->
  <Target Name="ReportCodeAnalysisResults" AfterTargets="RunCodeAnalysis" Condition="'$(RunCodeAnalysis)' == 'true' And '$(IsRunningOnTeamCity)' == 'true'">
    <Message Text="##teamcity[importData type='FxCop' path='$(CodeAnalysisLogFile)']" Importance="High" />
  </Target>
</Project>