The Welsh international failed to win back his first-team place from Paul Gerrard after suffering a back injury last season.
Ward will link up with former Forest team mates Darren Huckerby and Jim Brennan at Carrow Road and has signed a two-year deal.
Former Forest manager David Platt signed the former Mansfield man from nearby neighbours Notts County on a bosman free transfer.
He will also have to battle it out for a first-team place at Norwich against England international Robert Green and Scottish youngster Paul Gallacher.
