McVeigh, who spent the end of last season on loan at Burnley prior to his release from Carrow Road, had been linked with Ian Holloway's Plymouth Argyle. Instead, he will join an experienced Hatters line-up including fellow former Premiership players Paul Furlong, Chris Perry, Don Hutchison and Paul Peschisolido.
Northern Ireland international McVeigh spent seven seasons at Norwich following his move from Tottenham Hotspur. He played over 200 times and scored 39 goals.