I have looked through many web pages on the new Git integration in VS 2013 and they do not deal with adding an existing solution to Github. In fact I can\'t find much on us
Visual Studio should now ask your GitHub credentials and then proceed to upload your solution.
Since I have my Windows account connected to Visual Studio to work with Team Foundation I don't know if it works without an account, Visual Studio will keep track of who commits so if you are not logged in it will probably ask you to first.