Yes if was purchased to work on Verizon. Most cell services use a system called GSM, but not Verizon. Ours is an older system called CDMA ... supposedly better for range and clarity of calls but not compatible with other systems in the world. My new iPhone 5 was purchased for Verizon and works fine.
Maybe you did not really read the OP. They asked if an AT&T iPhone will work on Verizon. If it is an AT&T iPhone, it was obviously NOT purchased to work on Verizon, but on AT&T.