The 17-year-old is highly rated ad has been training with the Rochdale first team since he was 14.
Rochdale manager Brian Barry-Murphy told the club's website: "For Dan to come right through our Academy system and progress into the first-team environment with us is superb for everyone connected with the Club and the Academy. The move is a reward for his hard work and amazing attitude during that time.
"It also represents an excellent deal for the Football Club. When a Club comes in for one of our players, they have to do so with an offer that reflects the qualities of that player, which is something Norwich have done with Dan.
"I've got to know Dan and his family over a period of time. They're amazing people and its humbling to be connected to them. The way Dan approaches every challenge he faces is something everyone, including myself, can learn from.
"We'd like to wish Dan all the best for the future and will be keeping a keen eye on his progress at Norwich."