It is tremendously variable, and primarily depends on how long it takes your old carrier to release the number. Mine (ported from T-Mobile) took about an hour and a half. Some people report it taking less than an hour. Less than 12 hours is typical. More than 24 hours is unusual, unless you are porting a land line, which it doesn't sound like you are.
If you have been waiting for more than 24 hours, it is probably worth your while to call AT&T.