The 36-year-old, who played in only seven games last year after suffering a torn anterior cruciate knee ligament in 2010, helped the Patriots to Super Bowl glory in 2002, 2004 and 2005.
Faulk, a second-round selection in the 1999 NFL Draft, departs New England as the club's career leader in all-purpose yards with 12,349 and kick return yards with 5,041.
He ran for 3,607 yards and 16 touchdowns and caught 431 passes for 3,701 yards and 15 touchdowns in 161 career games for the Patriots.
"Kevin Faulk helped define the way an entire generation of Patriots fans have come to view and appreciate our brand of football," said Patriots chairman Robert Kraft.
"He worked so hard to get better every year. He was always one of the first to arrive in the building and among the last to leave."