Chadwick, who began his career at Manchester United, has played only once for the Canaries since signing on loan in November. He scored on his debut against Ipswich, but later sustained a knee injury which will rule him out until later this month.
The winger is believed to have cost in the region of £200,000 and will bring experience to the City side once he has recovered. He has been a Carrow Road target for some time, having narrowly failed to join last summer under Nigel Worthington.