Suh, 31, was released by the Miami Dolphins on Wednesday halfway through the six-year, $114.4 million free-agent contract he signed with the club in 2015.
A three-time first-team All-Pro, Suh started all 48 games in his seasons with the Dolphins and compiled 181 tackles (109 solo), 15.5 sacks, 13 passes defensed, two forced fumbles and one fumble recovery.
During his five seasons with the Detroit Lions, the 6-foot-4, 307-pound Suh emerged as one of the game's dominant defensive linemen, registering 36 of his 51.5 career sacks.
New Orleans, which has brought in cornerback Patrick Robinson and linebacker Demario Davis in free agency, also has $3 million more to spend as a result of an apparent settlement between the team and defensive tackle Nick Fairley.
A former teammate of Suh in Detroit, Fairley signed a four-year contract with the Saints a year ago but was unable to play last season after he was diagnosed with a heart condition during his physical.