Yes absolutely! Now that you are using ssh as the transport, you've done half the job.
GitHub and Gitlab are both remote(central) repositories. It all depends on the remote you are using to push your commits.
If you have created a project say, on GitHub, and cloned it, you will see that the remote (which is origin by default) points to the GitHub link. run $ git remote -v inside the project directory to inspect.
If you want to push the same project on GitLab, all you have to do is add another remote with a different name.
$ git remote add <different-remote-name> <gitlab-remote-link>
Now whenever you want to update a particular remote, just push to it.