Ian Rapoport of the NFL Network reported it's a $57.5 million deal with $33 million in guaranteed money.
Peat has spent his entire career with the Saints, who selected him with the 13th overall pick in the 2015 NFL draft. He's earned Pro Bowl selections in each of the past two seasons.
The 26-year-old Stanford product has recorded 65 appearances (60 starts) in five years with New Orleans.
"He's been one of our most versatile o-linemen, because he's played guard, he's played tackle," quarterback Drew Brees told reporters in February. "I can think of many situations, just mid-stream, mid-game where all of a sudden he's flip-flopping to tackle and then he's back at guard or whatever it might be."
Tackles Terron Armstead and Ryan Ramczyk both remain under contract for 2020, so Peat should once again slot in as a starting guard in 2019 along with Larry Warford. Erik McCoy will slot in at center to round out the offensive line.
Football Outsiders ranked the group first in run blocking and third in pass protection in 2019.
Peat's extension does come with some risk since he's never played all 16 games in a season and has missed a total of 15 games in five years because of injuries.
But the Saints' championship window is only guaranteed to stay open for as long as Brees, 41, remains under center, so re-signing Peat to a lucrative contract is a worthwhile chance to take.