For GitLab versions >= 8.9 (released in June 2016) you can use the built-in export and import project feature.
Please not that for the existing installations of GitLab, this option has to be enabled in the application settings (URL: /admin/application_settings)
under ‘Import sources’. You have to be a GitLab admin user to enable and use the import functionality.
Here is the feature complete documentation: https://gitlab.com/help/user/project/settings/import_export.md