Jenkins started 66 games in seven seasons with the Green Bay Packers. He had a career-high seven sacks in 11 games with the Super Bowl-champion Packers last year.
He can play defensive tackle or defensive end but has generally lined up inside throughout his career.
Bunkley was picked 14th overall in the first round of the 2006 draft.
The Eagles also re-signed unrestricted free agent linebacker Akeem Jordan.