It sounds like this is a personal account (not a business or government) so the port process will take up to 24 hours - do as suggested and it will be quicker. Keep in mind you will not be able to send or make calls during the porting process, though you should still receive text and phone calls.
I 2nd the suggestion to call and verify service has been cancelled with Verizon and then also make a note that if you don't get a final bill in a reasonable time that you call again and find out where it is. Also make sure your address is up to date as they will more than likely mail you a final bill. Don't forget about this, I've seen a few people come on here and say how they cancelled, thought they were finished paying and instead have owed a balance for years and now collections was after them.