The 28-year-old former Hull City defender has completed a move to join Chris Hughton at Carrow Road for an undisclosed fee, signing a two-year deal with the Canaries
The 28-year-old has penned a two-year deal at Carrow Road, bringing to an end a three-year spell with the Black Cats.
The centre-back suffered from repeated injury problems during his time at the Stadium of Light, but did manage to make 29 appearances last season.
"I'm delighted to be able to bring Michael into the squad as he is a player with a wealth of Premier League experience," Norwich manager Chris Hughton told the club's official website.
"At 28 years old he is joining us at a good age, and I'm happy to have been able to welcome him to Norwich City.
"Like with [new signings Robert] Snodgrass, [Jacob] Butterfield, and [Steven] Whittaker, it’s nice to bring players in with a good amount of time left in pre-season so they are able to gel with the squad ahead of the first game of the season."
Turner was allowed to leave Sunderland despite the news that fellow defender Wes Brown had suffered a knee injury during the friendly against Groningen.
"I'm delighted," Turner enthused. "The deal is all signed now and I'm happy to be here.
"The manager needs to want you first and foremost to get the ball rolling, and that was the key with Chris Hughton.
"I've heard a lot of people say good things about what he does and has done in the game, so I'm just pleased to be a part of his team.
"I was really impressed with Norwich last season. I was on the bench for the game at Carrow Road, and I got to see them play, so I was impressed with the players, the stadium, and the whole set up of the club.
"I've picked up a lot of experience throughout my career, and hopefully I can add a bit to the squad here.
"I feel good. Last year I played just shy of 30 games, and now that I've come back to pre-season I feel stronger than ever."