To prevent the packages folder from being added to Team Foundation Version Control in Visual Studio 2015 you can add a .nuget folder in your solution folder. In the .nuget folder add a file named NuGet.config with the following content:
<?xml version="1.0" encoding="utf-8"?>
<add key="disableSourceControlIntegration" value="true" />
This tells Nuget to not even call Visual Studio about the changes to the packages folder.
For TFS 2012 and later also add a .tfignore file in your solution folder with the following content:
## Ignore the NuGet packages folder in the root of the repository
#include package target files which may be required for msbuild
This will ignore changes to the packages folder.