Yes you can. That is exactly what I did when I got my iPhone.
Most of the people I asked told me that I couldnt do it, but I did and you should be able to too.
When you port your number to AT&T verizon automaticly ends your contract with them. However if you call customer service or go talk to a store and talk to a representative they will more than likly reactivate your contract to keep you as a customer.
Technicaly they are not suposed to keep you unless they bring your number back with you, but if you tell them your situation they should let you get a new number.
Dont let the cell company set all the terms, there is always a way to get what you want.