Hicks, 28, is coming off a season in which he played for the New York Giants, the same team that drafted him in 2009, for the last six games and posted seven receptions for 54 yards.
As a member of the Indianapolis Colts in the 2014 season, he caught 38 passes for 405 yards and four touchdowns.
Nicks tweeted a photo of the Saints logo on Wednesday:
He joins a wide receivers staff that includes Brandon Coleman, Brandin Cooks, Willie Snead and second-round draft pick Michael Thomas.
He has 356 catches for 5,081 yards and 31 touchdowns in his career.