"I'm delighted to be able to bring Michael into the squad as he is a player with a wealth of Premier League experience," 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 Snodgrass, Butterfield, and 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 added: "I'm delighted. 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."