Colston played 10 seasons for the Saints, who drafted him in the seventh round in 2006. He has 711 career receptions for 9,759 yards and 72 touchdowns.
Coston, who will turn 33 in June, had 45 receptions for 520 yards and four touchdowns in 13 games, including five starts, in 2015.
The move frees up about $3.2 million in salary cap savings.
With Colston's release, only three players remain from the Saints' Super Bowl victory following the 2009 season: quarterback Drew Brees, offensive tackle Zach Strief and punter Thomas Morstead.