The ban is now headed to Governor Bev Perdue's desk for her signature.
However, objections from the bill's opponents say the law would be unenforceable, because it would be difficult for police to determine when someone was using a cell phone to send text messages or e-mail instead of legally dialing a phone number.
If the ban becomes law, it would take effect Dec. 1.
A driver who gets caught texting while behind the wheel could face a $100 fine. But drivers would not receive points on their drivers license or insurance if they are caught.