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.
Speaking on his move to the Barclays Premier League side, Redmond told canaries.co.uk: "I'm very happy. It looks like a fantastic club, I'm just looking forward to getting started now."
He added: "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."
Redmond came through the Birmingham Academy and played under Hughton when he was manager at St Andrew's, which included a run in the Europa League for the Championship club.
The winger, who featured for the England under-21s in this summer's European Championship, is looking forward to linking up with his old manager again, this time in the top flight.
"He was very influential on my career at Birmingham. He gave me the chance to play and the chance to express myself every time that I stepped on to the field and I feel like on the bigger stage he will do exactly the same thing," Redmond added.
"I would probably say I have played some of my best football under him so far.
"Last season was a good one for me in terms of goals and assists and just general performances.
"Hopefully I can continue the form that I left off with last season at Birmingham."
Source: PA
Source: PA