That was what I was getting out of this after re-reading the thread title.
If you cancel, get a phone on Verizon, then try to port your ATT number to it, you'll probably be SOL. That number should just go back into their pool of available numbers for anyone to pick up. If someone else gets it, you're screwed.
So you'll want to get the account BEFORE you cancel with ATT.
Open the account with Verizon and tell them to port your number. When that happens, your account with AT&T will automatically close and you will receive a final bill including any termination fee if you owe them one.