The 23-year-old has been first-choice stopper for the League Two outfit for the last 18 months and caught the eye when he played against Wolves at Molineux last season, saving a penalty in the EFL Cup.
Wolves had already been in the market for new goalkeepers this summer but were forced to up their efforts following the tragic news last week that long-standing number one Carl Ikeme has been diagnosed with leukaemia.
"I am buzzing to be here," said Norris, who had been with Cambridge for five years. "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.
"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."
Having completed the deal, Norris will now fly out to Austria to join his teammates for their pre-season training camp.