The 25-year-old had been set for a move to Championship side QPR before Chris Hughton swooped to make Hooper his seventh signing of the close-season.
Hooper, who won two Scottish league titles and two Scottish Cups during his time at Celtic Park, was also the club's top scorer for the last three seasons.
The former Scunthorpe striker had been linked with a move to Carrow Road for a number of months but was happy to finally have his future agreed.
"There's been a lot of speculation going back to January and I'm pleased to have finally put pen to paper and joined Norwich," Hooper told the club's official website.
"I can't wait to get down to work, to get training with the lads and working with the coaching staff. I knew Chris Hughton and Colin Calderwood from my youth days at Spurs so it will be great to be back working with them in the Premier League.
"I have scored goals at every level I have played at and the challenge of playing in the Premier League is really exciting to me."
Hooper made 137 appearances during his time at Celtic, scoring 82 goals.
