Norwich agreed compensation with Hughton's former club Birmingham City yesterday before talking with the ex-Republic of Ireland international today. He will be followed to Carrow Road by assistant manager Colin Calderwood, first-team coach Paul Trollope and chief scout Ewan Chester.
On his departure, acting Birmingham chairman Peter Pannu said: "We'd like to thank Chris and his team for their efforts over the last 12 months and they leave with our best wishes.
"Chris is a great man and a proven manager and we didn't want to stand in his way when Norwich made an approach with the offer of a top-flight managerial position.
"We will now actively seek a new coaching team to build on the good work done during the 2011-12 season."
Hughton led Birmingham into the Championship playoffs last season, only to see his side eliminated at the semi-final stage by Blackpool.
The former Tottenham player has Premier League experience as a manager, having been in charge of Newcastle for part of the 2010-11 season after guiding them to the Championship title the season before.
Hughton's overall managerial record has seen him take charge of 149 games, winning 69, drawing 42 and losing 38, a win percentage of over 46%.