The 25 year old has put pen to paper on a three-year contract with the Canaries, who have the option of keeping him for a further year.
Queens Park Rangers had also been interested in signing the striker, who scored sixty-three goals in ninety-five appearances since arriving in the Scottish Premier League in 2010.
The former Scunthorpe United man also boasts Champions League experience, and scored four goals during last season’s campaign, where Celtic reached the last sixteen of the competition.
He began his youth career with Tottenham Hotspur, where he worked under current Norwich boss Chris Hughton and his assistant Colin Calderwood.
Hooper becomes the eighth new arrival at Carrow Road this summer, joining fellow centre-forward Ricky van Wolfswinkel, midfielders Leroy Fer and Nathan Redmond, defenders Martin Olsson, Semi Ajayi and Javier Garrido and goalkeeper Carlo Nash.