Cantwell has signed a long-term contract at Ibrox, bringing an end to his 14-year association with the Canaries.
The 24-year-old came through the Norwich youth ranks to make 129 appearances for the senior team, scoring 14 goals.
He was instrumental in two promotions to the Premier League that all resulted in relegation.
Cantwell was sent out on loan to Bournemouth for the second half of the 2021/2022 season and has failed to score in 18 championship games for Norwich this season.
The former England u-21 international is now set for a new challenge in Scotland.
Speaking to RangersTV on his arrival at Ibrox, Cantwell said: "I am delighted and I feel very proud. This is obviously a massive football club and I am delighted to get going and to get started.
"This is a massive club and there is a massive responsibility when you sign for Rangers to be the player that the fans want to see.
"They want to see a player that works hard and a player that can win them games which is very important and that is something I am hoping I can bring."
Rangers manager Michael Beale added: "I am extremely happy to welcome Todd to Rangers. He is a player that is fully aligned to our playing style and we believe he will be a key player for the club in the coming seasons.
"I am looking forward to working with him on the pitch this week and integrating him into our fantastic football club."
Sporting Director Ross Wilson continued: "We are delighted to welcome Todd to Rangers. Michael and I have spent a lot of time talking with Todd, and indeed with others about his quality and what he can bring to our squad. We are excited to have him start with the group this week."