The new contract awaits NFL approval, The (New Orleans) Times-Picayune reported.
Payton will be paid about $7.5 million a year for five seasons, CBS Sports reported.
The Saints decided to stick with Payton despite his having to sit out the 2012 season under an NFL suspension imposed for the team's bounty scandal. The league had voided his original contract extension announced in September 2011.
The NFL had said Payton would be eligible to apply for reinstatement Feb. 4, but the newspaper said league officials declined to comment Friday night whether that was still the effective date.
"Very happy that it is offical. Never had any doubts though," Saints quarterback Drew Brees said via text.
Likewise, punter Thomas Morstead expressed his approval via Twitter: "BOOM HE'S BACK!!!!"
The Saints went 2-4 with offensive line coach Aaron Kromer as interim coach and are 5-4 under Joe Vitt, a Payton assistant who served a six-game suspension.
Payton, who was suspended for the alleged reward program for New Orleans defensive players who purposely injured members of opposing teams, lives in the Dallas area during the off-season. With the Cowboys struggling during the first half of the current season, there had been speculation he might be changing jobs in 2013.
His original contract extension had given him the right to void the contract if New Orleans General Manager Mickey Loomis left the club.
Payton took over as New Orleans coach in 2006 and led the Saints to the Super Bowl title at the end of the 2009 season with a 31-17 victory over Indianapolis.
New Orleans plays its regular-season finale Sunday against Carolina.