Hooper has been Celtic's leading goalscorer for the last three seasons, having joined from Scunthorpe in 2010 for £2.4million.
Celtic manager Neil Lennon today described Hooper as the club's best striker since Henrik Larsson and said his departure was a "huge loss" for the Bhoys.
Hooper told the Norwich website: "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.
"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."