Hooper looked set for a move to Championship side QPR, with the Hoops understood to have agreed a fee in the region of £5million for the 25-year-old on Wednesday.
But Norwich have been in the hunt for Hooper for some time, with manager Chris Hughton seeing several bids rejected in the January transfer window, while Hull City also missed out with their approach in June.
Hughton may yet get his man and former Southend and Scunthorpe forward Hooper could be playing in the Premier League come the start of the new season.
The news will come as a blow to QPR boss Harry Redknapp, who admitted earlier he expected their swoop to go through without a hitch.
Redknapp had said: "It looks like it's on its way to being done. Negotiations have gone well.
"He's a finisher. He'll score goals in the Championship; I'm absolutely certain of that.
"He's gone to Celtic; one of the biggest clubs in the world and he's scored goals. He's scored goals in the Champions League.
"He's in the last year of his contract, so it's a good deal for everybody. It's good for Celtic to get the kind of money they are getting and hopefully it will be a great deal for QPR.
"If he can come here and get 25 goals next season, then we will have a real chance of getting out of the division."
Hooper arrived at Celtic Park from Scunthorpe for a fee of around £2.4million in July 2010 and has scored 82 goals in 138 appearances.
Nottingham Forest were also in contact over a possible transfer though Hoops manager Neil Lennon had not given up hope of keeping his prolific marksman.
Hooper has been the club's leading marksman in all three of his Parkhead seasons but is in the final year of his contract and could leave for free in 12 months' time.