The striker scored 82 goals in 137 appearances during his three seasons in Scotland, but that record was not enough to earn an international call-up.
Hooper, who "was close" to joining QPR before signing a three-year deal with City last week, hopes that will change if he can continue finding the net in the Premier League.
He said: "I wanted to play in the Premier League and to try to get an England call-up. I think there's a good chance of that.
"You don't really get a look in up there. Down here you've got more chance. The main thing is playing, getting on the pitch first, and doing what I do.
"To play for your country is anyone's dream, but my first dream is to play in the Premier League.
"I had the Champions League at Celtic and they wanted to keep me. It was a tough decision, but I'm here now and I'm happy."
Norwich boss Chris Hughton said: "He's got to play well enough for Norwich City Football Club and score goals and prove that he can do it in this very, very difficult league.
"That's the reason why he's here and that's the wonderful challenge that he has."