The 23-year-old Norris, who saved a penalty at Molineux in the EFL Cup last season, has put pen to paper on a three-year contract, with Wolves holding an option for a further year.
Norris will now join fellow recent goalkeeping signing John Ruddy in the battle for the shirt along with Harry Burgoyne and Jack Ruddy.
“I am buzzing to be here,” said Norris.
“This is a fantastic opportunity at a fantastic football club and was something I just couldn’t say no to.
“I have been playing regularly for Cambridge over the last 18 months or so and now know I have a battle for a place which is a great challenge.
“I used to watch John a lot growing up – he used to play for Cambridge United as well – and it is going to be great for me to be working with him at Wolves.
“Cambridge have been fantastic with me both throughout my career and also the process of this move.
“They brought the right people in to develop me and it has been a fantastic experience for me.
“I am a little bit sad to be leaving but obviously I am leaving for a great opportunity and a new challenge here at Wolves.”
Norris, now set to fly out to Austria to join up with the pre-season tour, is looking forward to meeting his new team-mates, as well as working with goalkeeping coach Rui Barbosa.
“I have been told about the goalkeepers the coach here has worked with and he has a massively impressive CV,” he added.
“I am looking forward to getting in the building and learning as much as I can from him and the other goalkeepers as well.
“It will be good to get out to Austria and be together as a squad for a good week or so.
“It will be good to integrate with the lads and get me off to a good start.”
Norris, born in Watford, started out in non-league before joining Cambridge in the summer of 2012.
He was loaned back to his previous club Royston Town for the 2012/13 campaign before making his Cambridge breakthrough in the latter stages of the following season, making a total of 15 league appearances as the U’s returned to the Football League via the Conference play offs.
Norris spent the first half of the 2015/16 season on loan back in the National League with Braintree, including being named the league’s Player of the Month in October after keeping four clean sheets in six games.
Recalled to Cambridge by new boss Shaun Derry, he kept nine clean sheets in 21 games as the club finished ninth in League Two.
He was then first choice keeper for last season, making 54 appearances in all competitions, including at Molineux in Cambridge’s 2-1 defeat against Wolves.
His penalty save from James Henry was one of many made by Norris during the campaign.
“It was nice to save the penalty – but we lost the game so it didn’t really matter!” adds Norris.
“I saved a few last season and got a bit of attention for those penalty saves although I’d rather we hadn’t given them away.
“Hopefully the fans who were there at Molineux might just remember me and I am looking forward now to trying to get in the team and having them on my side.
“Wolves are an absolute giant of a club – I drove all the way here with a smile on my face and am really excited about what lies ahead.”
