Graham, the 13th overall pick in April's NFL Draft, tore his anterior cruciate ligament during Sunday night's 30-27 win at Dallas.
Philadelphia sent its first-round pick (24th overall) and a pair of third-round selections (Nos. 70 and 87) to Denver to move up and select Graham. He had three sacks.
Bradley has been plagued by injuries the past two seasons -- he sustained a concussion in Week 1 and missed the next game. He missed all of last season due to a torn anterior cruciate ligament.
The Associated Press contributed to this report.