The deal will be worth $26 million over four years, with $14 million guaranteed, a source told ESPN's Adam Caplan, confirming an earlier report by the NFL Network.
Graham, who turns 27 on April 3, began his career as a defensive end in the Eagles' 4-3 scheme. As a rookie, the former first-round pick had three quarterback sacks. In 2011, Graham appeared in just three games before tearing the ACL in his right knee. He returned for the 2012 season, registering 5.5 sacks as the Eagles went 4-12.
That 4-12 record brought about a coaching change with Chip Kelly hired to replace Andy Reid. Kelly hired defensive coordinator Bill Davis to run a 3-4 scheme. The 6-foot-2, 265-pound Graham was not big enough to play on the line in the new defense and was moved to outside linebacker.
In 2013, Graham struggled with the transition. He played in 16 games without making a start, and he had three sacks. In 2014, Graham played in just 43 percent of Eagles defensive plays. But he was very productive, equaling his career-high with 5.5 sacks. Graham was credited with 18 hurries and four forced fumbles.
Graham said after the season that he considered himself a Philadelphian and hoped to return to the Eagles. But the Detroit native also wants to start, whether at outside linebacker or at defensive end.
ESPN.com Eagles reporter Phil Sheridan contributed to this report.