The move means second-round draft choice Jimmy Garoppolo will be the backup to two-time MVP Tom Brady. Mallett back up Harvard product Ryan Fitzpatrick in Houston.
Originally a third-round draft pick from Arkansas, Mallett played four games in three years with the Patriots, completing one pass.
The Patriots picked Garoppolo this year in the second round — the highest coach Bill Belichick has selected a quarterback in New England. In the preseason, Garoppolo was 46 for 79 for 618 yards, five touchdowns and an interception; Mallett was 14 for 26 for 161 yards and a touchdown.
Also Sunday, the Patriots claimed defensive linemen Bruce Gaston and Kelcy Quarles off waivers. New England released linebacker Chris White.