You can import your existing GitLab.com projects to your GitLab instance. But keep in mind that it is possible only if GitLab support is enabled on your GitLab instance. You can read more about GitLab support here To get to the importer page you need to go to "New project" page.
Note: If you are interested in importing Wiki and Merge Request data to your new instance, you'll need to follow the instructions for project export
Click on the "Import projects from GitLab.com" link and you will be redirected to GitLab.com for permission to access your projects. After accepting, you'll be automatically redirected to the importer.
To import a project, you can simple click "Import". The importer will import your repository and issues. Once the importer is done, a new GitLab project will be created with your imported data.