The deal came with just an hour to go in the Premier League's deadline day, as Maddison will play the rest of the 2015-16 season on loan with Coventry.
Maddison was sold to his new club for an undisclosed fee.
A 19-year-old, Maddison has scored two goals for Coventry, who play in England's League One, two levels beneath the Premier League where Norwich play.
The youngster seems thrilled to join the Premier League side.
"I've been working hard towards achieving this goal, and I'm delighted to be signing for a club the size and stature of Norwich," he told the team's official website. "They are a club moving in the right direction, and I'm looking forward to progressing my career there after finishing this season at Coventry."
Norwich manager Alex Neil spoke on his newest option at midfield.
"We’re delighted to sign James, as he is a fantastic prospect who has already made a mark at Coventry at such a young age," Neil said. "He has real potential to develop, making this deal one we’re really pleased to get over the line."
Coventry executive vice chairman Chris Anderson wasn't happy to see Maddison go.
"We're sad to see James leave the club but wish him all the best for the future," Anderson told CCFC.co.uk. "It was with great reluctance that we accepted Norwich's offer, but the deal provides a level of revenue which will help the club grow in the future to build a successful squad beyond the rest of this season."
The midfielder is Norwich's eighth signing of the January transfer window as they look to improve their standing in the Premier League.
Maddison made his League One debut with Coventry as a 17-year-old and has made 31 appearances in all competitions since, scoring four goals. He's scored two goals this season from the midfield.
For a player his age, Maddison has shown solid vision in the midfield that can be the motor of an attack one day at Carrow Road. He also holds a scoring touch that could add another dimension of offensive play for Norwich.
Sitting in 17th place through 23 matches, Norwich are just three points above the relegation zone. Only five teams have scored fewer goals than the Canaries, who look to have acquired a midfielder for the future.
The only question is whether that new midfielder will be playing his football in the Premier League or Championship once he is able to put the yellow and green on.
Stats courtesy of BBC.com