Jordan's deal is worth $52.5 million and includes over $42 million guaranteed, sources told ESPN's Adam Schefter.
The agreement keeps Jordan, who had two years left on his previous deal, tied to the Saints through the 2023 season. The soon-to-be 30-year-old will earn $74.5 million if he plays out the next five seasons and hits all his incentives.
Jordan posted 12 sacks in 2018 and has reached the double-digit sack mark in four of his eight NFL campaigns. He hasn't missed a game since entering the league as the Saints' first-round pick in 2011.
A four-time Pro Bowler, Jordan ranks fourth in team history with 71.5 career sacks.