Cantwell joins the Ibrox club after making 129 appearances for the Canaries, which included six goals and two assists in 45 games in the Premier League.
He has also had loan spells with Bournemouth and Fortuna Sittard.
The 24-year-old becomes Rangers boss Mick Beale's first signing since he returned to the club as manager.
Speaking to Rangers TV, Cantwell stated he was delighted to join the Glasgow giants.
"I am delighted and I feel very proud," Cantwell said.
"The fans want to see a player that works hard and can win them games and that is something I am hoping I can bring.
"This is obviously a massive football club and I am delighted to get started."
Cantwell could be in line to make his debut for Rangers against St Johnstone at Ibrox on Saturday.
