Andersen would emerge as one of the greatest Place Kickers in the history of the game. A member of both the 1980s and 1990s All-Decade Team, Andersen was a six-time Pro Bowl Selection as a Saint, and he would also collect two First Team and two Second Team All-Pro Selections. With New Orleans, Andersen accumulated 1,318 Points, a still-standing franchise record.
After he was released due to salary cap reasons, he played for another 12 seasons. At the time of his retirement, Andersen was the all-time leader in Points and Field Goals, though Adam Vinatieri has since passed that. Andersen would enter the Saints Ring of Honor in 2015 and the Pro Football Hall of Fame in 2017.