Terms of the deal were not disclosed by the team for the 27-year-old Bolden, who was an unrestricted free agent.
Bolden's contributions were felt primarily on special teams in 2016. He has 20 career special teams tackles and one blocked punt during his five seasons with New England.
Bolden had just one rushing attempt for four yards and two receptions for 15 yards while playing in 14 games last season. He has 203 carries for 845 yards and six touchdowns and 46 receptions for 366 yards and two scores in 67 career contests with the Patriots.