The 25-year-old, who scored 31 goals for the Scottish champions last season, becomes the Canaries' seventh summer signing after he agreed personal terms and passed a medical at Carrow Road.
Norwich manager Chris Hughton first tried to sign Hooper in January and the Barclays Premier League club fought off competition from QPR to finally land the prolific frontman.
Hooper has signed a three-year deal with Norwich having an option on a further year. The fee was undisclosed.
Hooper has been Celtic's leading goalscorer for the last three seasons, having joined from Scunthorpe in 2010 for B£2.4million.
Celtic manager Neil Lennon has 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, www.canaries.co.uk: "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."
Hooper is the second striker recruited this summer by Hughton, following the record signing of Dutch international Ricky Van Wolfswinkel for £8.5million from Sporting Lisbon.
- Sports & Recreation
- Premier League
- Chris Hughton