The veteran kicker was signed to a one-year, $955,000 deal, according to the NFL Players Association's website.
With 13 seasons under his belt, Graham landed with the Saints in December after New Orleans waived Garrett Hartley. Going 2 for 2 in the regular season, Graham proceeded to punch in four of his six field-goal attempts in the playoffs. That included the game-winner against the Philadelphia Eagles, but also two costly misses from 45 and 48 yards in January's loss to the Seattle Seahawks.
Graham's only competition on the roster is little-known Derek Dimke, meaning the journeyman kicker is a good bet to play into his age-37 season.
New Orleans also re-signed right tackle Bryce Harris to a one-year, exclusive-rights free-agent deal of $570,000. The 25-year-old lineman started one game last year but appeared in all 16 regular-season contests as an extra body up front, a special-teams contributor and an occasional blocking tight end.