The 19-year-old, who joins for an undisclosed fee, is the Canaries' third signing of the summer following the arrivals of Ricky van Wolfswinkel and Javier Garrido.
Redmond told canaries.co.uk: "I'm very happy. It looks like a fantastic club, I'm just looking forward to getting started now.
"I know that there is only one football club in this city and it has an excellent fan base.
"The people around the football club and in the city that I have spoken to so far have attracted me to this club so much, it's made me realise just how much this club means to the people of this city."