The Scotland defender was available as a free agent after rejecting a move to the Ibrox club's newco and becomes Chris Hughton's first signing at Carrow Road
The 28-year-old Scotland international was a free agent after refusing to transfer his contract over to the Rangers newco owned by Charles Green.
The versatile defender has signed a four-year deal at Carrow Road but must now await international clearance to seal the move.
Hughton told the club's official website: "In Steven we have a player who is very versatile - he can play anywhere across the back four and anywhere across midfield, so there's plenty of versatility there.
"It's probably a good time for him. Sometimes it is time to move on to a different club, and go there with a lot of enthausiasm, and he has international experience too.
"He has of course been used to playing at a very high level when he was at Rangers, and in a lot of big games with a passionate crowd behind him. So the stage of the Premier League is certainly one that won't faze him with his experience."
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He said: "All of my experience to date has been in Scotland so I'm really looking forward to the challenge of playing in the Premier League, I'm very excited about it.
"When I spoke to Chris Hughton I was very impressed with his plans to progress Norwich City and everyone I've spoken to in the game has had nothing but praise for the Club and the city of Norwich.
"I know Simon Lappin from a few years back and of course I know Russell Martin from Scotland and I'm looking forward to meeting up with the squad and the staff."Whittaker has 15 international caps for Scotland and was an integral part of the Rangers side who were beaten finalists in the 2008 Uefa Cup.