Chung, out of Oregon, was one of four players drafted in the second round by the Patriots, who traded their first-round pick. He was taken with the 34th pick overall, obtained from the Kansas City Chiefs for quarterback Matt Cassel and linebacker Mike Vrabel.
Details of the contract were not disclosed. The Patriots other three second-round picks signed four-year deals. They are nose tackle Ron Brace of Boston College, cornerback Darius Butler of Connecticut and offensive tackle Sebastian Vollmer of Houston.
The Patriots released safety Antwain Spann, a three-year veteran.
Their only draft picks without agreements are third-rounder Tyrone McKenzie, a linebacker from South Florida, and sixth-rounder Jake Ingram, a long snapper from Hawaii. McKenzie tore the anterior cruciate ligament in his right knee in rookie minicamp in May and is out for the season.
Chung started the most games of any defensive player in his school's history. His 51 consecutive starts are tied for the Oregon record for players at any position.
The Patriots hold their first full-squad training camp practices Thursday. Rookies reported Sunday.
Spann played in 19 regular-season and three postseason games for the Patriots the past three seasons.