The 53-year-old Blues boss takes over the managers post at Carrow Road vacated by Paul Lambert who became the new boss at Aston Villa last week.
Three of Hughton's backroom staff will be moving with him to Carrow Road after Blues confirmed that they had also accepted a compensation fee for assistant boss Colin Calderwood, first team coach Paul Trollope and chief scout Ewan Chester.
"We'd like to thank Chris and his team for their efforts over the last 12 months and they leave with our best wishes," acting chairman Peter Pannu told the club's official website, bcfc.com.
"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."