On LinkedIn it has always been pretty easy to promote your group to your email list. Sending out a bulk invite has been a common tactic for owners looking to grow their group rapidly. Doing likewise on a Facebook page hasn't been as easy. The functionality did exist previously, but it was hidden behind the label 'tell your fans', so it wasn't particularly obvious that this was what it entailed.
Now however the label reads 'invite email contacts'
To use the feature you simply need to upload a CSV file of your contacts. You can upload 5,000 at a time and send an invite to your contact list.