Roeder succeeds Peter Grant who was axed earlier this month following the Canaries' dreadful start to the season.
Results on the pitch have not improved since Grant's departure and Saturday's defeat at West Brom left the club rooted to the foot of the Championship table.
Roeder, who has signed a two-and-a-half year contract at Carrow Road, was sacked by Newcastle in May. Caretaker manager Jim Duffy has left the club.