The proposed solution does not work for me as well.
I added my GitHub account under Xcode -> Settings -> Accounts. I also added my Author Name and Author Email under Xcode -> Settings -> Source Control.
I made changes & went to Integrate -> Stage All Changes (this worked). Next, I went to Integrate -> Commit... and the screen below opens with the commit button greyed out.
I know I can use terminal to commit my changes. I am trying to get the source control integration working on my project.