Simple and pretty neat trick:
Lets say your project repository in my
SampleProjectgit remote rename origin bitbucket git remote add origin https://github.com/sample/
SampleProject.git git push origin master
git remote rm bitbucket
It'll only remove your local reference not your origin repository.
You'll notice that your tags are still not visible in github. You may need to run single command on terminal:
git push origin --tags -f