The teenager is the Canaries' third signing of the summer following the arrivals of Javier Garrido and Ricky van Wolfswinkel and says he is thrilled with the move.
“I'm very happy. It looks like a fantastic club, I'm just looking forward to getting started now," he told the club's official website.
|11/2||Norwich are 11/2 with William Hill to finish in the top 10 next season
The switch sees Redmond reunited with manager Chris Hughton after the pair worked together at Birmingham and the Canaries boss admitted the club had been monitoring Redmond for some time.
"Nathan is a young and exciting player that I had the pleasure of working with at Birmingham. He is a player that was of interest to us for some time and the situation has now come about that we can get him on our terms," he said.
“He's someone we can bring in to the forward areas and primarily has played on either wing in his career so far, but can also play off the front. He's very keen to develop his own game, he's one of these lads that likes to be on the training pitch and is usually one of the last ones off the training pitch.
“I'm sure the move won't phase him but this is still a part of his development and one he is very much looking forward to."