Short howto move an repository from one remote origin to another.
Step 1, make sure everything is synced before you begin.
git pull
git push
Step 2. Check what your current remote origin is
$ git remote -v
origin https://old/repository (fetch)
origin https://old/repository (push)
Step 3. Set your new remote origin
git remote set-url origin ssh://new/repository
Step 4. Verify
$ git remote -v
origin ssh://new/repository (fetch)
origin ssh://new/repository (push)