The deal is worth $57.5 million, with $33 million guaranteed, a source told ESPN, confirming a report by NFL Network.
Peat said there was some interest from other teams. But, "ever since I was drafted here, I wanted to play my whole career with the Saints."
"My intentions were always to come back to New Orleans," Peat said. "I've loved and enjoyed my time here. It's a first-class organization and a great locker room. And I feel like we've been building something special the past few years. So I'm just really happy how it turned out."
Peat, who turned 26 in November, is a former first-round draft pick and a two-time Pro Bowler after being selected as an alternate in each of the past two seasons.
The 6-foot-7, 316-pounder has started 64 games for the Saints, including the playoffs, during his five-year career. He has primarily played left guard. But he has also filled in on multiple occasions as the Saints' backup left tackle, which is where he played at Stanford before being drafted with the 13th overall pick in 2015.
Peat had his best two seasons in 2016 and 2017, and he was a key reason why the Saints' offense ranked among the NFL's top two in both yards per rush and yards per pass attempt in 2017. He has battled some injuries and inconsistency since then, however, missing six games with a broken arm last season. He also played through a broken hand during the 2018 playoffs.
His father, Todd Peat Sr., played guard in the NFL for six seasons with the St. Louis/Phoenix Cardinals and the Los Angeles Raiders.