The Saints had released Fleener just two seasons into his five-year, $36 million contract with a failed physical designation. He sustained his fifth career concussion in Week 12 of the 2017 season.
"He's still working through the process of getting cleared and he's still working through being without symptoms, but I also felt like for the team it was something that was going to be best for us," Payton said.
Fleener recorded 72 receptions for 926 yards and five touchdowns in 27 games since joining the Saints as a free agent in 2016.
The 29-year-old Fleener posted a career-low single-season total in catches (22) to go along with 295 receiving yards and two scores in 11 games in 2017.
Fleener spent his first four years with the Indianapolis Colts after being drafted in the second round out of Stanford. He has 255 catches for 3,080 yards and 23 touchdowns in his six-year career.
The Saints signed Benjamin Watson as a free agent this offseason to join Josh Hill and Michael Hoomanawanui among others at the tight end position.