The key lies in when you create the project in eclipse.
First step, you create the Java project in eclipse. Right click on the project and choose Team > Share>Git.
In the Configure Git Repository dialog, ensure that you select the option to create the Repository in the parent folder of the project..
Then you can push to github.
N.B: Eclipse will give you a warning about putting git repositories in your workspace. So when you create your project, set your project directory outside the default workspace.
Simple Steps:
-Open Eclipse.
Select Project which you want to push on github->rightclick.
select Team->share Project->Git->Create repository->finish.(it will ask to login in Git account(popup).
Right click again to Project->Team->commit.
you are done