The deal is worth up to $8 million, agent Drew Rosenhaus told ESPN's Adam Schefter.
The Seattle Seahawks released Dunlap on March 18 as their defense continues to transition to more of a 3-4 structure up front. Dunlap is more of a traditional 4-3 defensive end, which likely was a factor in his release.
He had one year remaining on a two-year, $13.6 million deal signed prior to the 2021 season. He was set to make up to $5.1 million in 2022.
The 33-year-old Dunlap was the Seahawks' most accomplished edge rusher and was coming off a strong finish in which he recorded eight sacks over the final six games. But that was after an unproductive first half in which he saw his playing time dwindle. He finished with 8.5 sacks last season.
Dunlap spent his first 10½ seasons with the Cincinnati Bengals, who drafted him in the second round out of Florida in 2010. The Seahawks acquired him via a midseason trade ahead of the 2020 deadline.
His 96 sacks are eighth most among active NFL players.
ESPN's Adam Teicher and Brady Henderson contributed to this report.