Norwich manager Glenn Roeder has made four permanent and three loan signings this summer, and said he was delighted to tie up the deal to sign Bell.
"David is a player, like others we have secured this summer, who we've been following for some time," said Roeder.
"We've tracked David's progress over the last season and we've been very impressed with his spell on loan at Leicester in difficult circumstances for that club."
Bell joins Sammy Clingan, Wes Hoolahan, Dejan Stefanovic, Elliott Omozusi, Ryan Bertrand and Arturo Lupoli as the new faces at Carrow Road.
