We use Visual Studio 2010 as our primary IDE for code development.
And recently the Team Foundation Server was upgraded to 2013.
And we were soon unable to connet and add Team Projects in VS 2010.
After doing some research I found a URL which instructed to download Team Explorer for 2012.
Sure enough the application loaded after install and pointed to the new TFS server.
Was able to create a new Team Project - success!