The England under-21 international has signed a three-and-a-half-year deal at Carrow Road but will immediately be sent back on loan to London Road, where he will remain until February 28.
The 21-year-old should be available to make his debut for the Canaries at Stoke on March 3, but will be ineligible to compete in City’s FA Cup run should they still be in the competition when he finally arrives at the club.
Speaking to the club’s official website, manager Paul Lambert said: “I'm delighted we have signed Ryan. He's made a bright start to his career at Grimsby and Peterborough, he's an England under-21 international and he's got so much potential.
“He can play, he's got great vision, he's comfortable on the ball, and he's a good age too.
“He'll be staying at Peterborough initially but will join us in time to be available for the Stoke game, and when he does come in he will provide more competition for places in defence, which is something you want to have right throughout the squad.
“I'm really pleased the deal has been done.”
Bennett signed permanently for Posh in January 2010 from Grimsby Town, and it has been reported that the Mariners will receive a slice of the transfer fee.