The forward, 22, passed a medical at Parkhead on Monday and the move was announced on Tuesday morning. The fee is believed to be £2.4million.
He sat out United's pre-season games as a move away from Glanford Park became inevitable, meaning his first proper taste of football could come against Braga on Wednesday.
"I don't know about playing him, but he will be in the squad," said Neil Lennon, the Celtic manager.
"He has been on our radar for a while. His record is very good. It's not just goals, he can play a bit as well and there were a lot of clubs after him."
Hooper joined his new teammates at Glasgow Airport on Tuesday morning to fly to Portugal.
The jump from Glanford Park is highlighted as it will be the first time he has left the United Kingdom for a match.
"I'm a little bit nervous, it's the first time I've travelled abroad for a game. But I am looking forward to it and ready to meet my teammates," he said.
"I`m ready to come on. I haven`t really played a game. I`ve been training really hard, double sessions, but I`m ready to come on and score goal.
"I am very confident that I can score goals for this club, I cannot wait to start playing."
Hooper is the sixth new signing of the summer at Parkhead, following Charlie Mulgrew, Efrain Juarez, Cha Du-Ri, Joe Ledley and Daryl Murphy.
Lennon has also held talks with David James, the England goalkeeper who is available on a free transfer after leaving Portsmouth.