The team released veteran cornerback Antwaun Molden to make room for the former Seattle Seahawks starter.
Trufant, a first-round draft pick in 2003, is entering his 11th season in the NFL. He has started 125 games, totaling 638 tackles and 21 interceptions. He played the last four seasons under Bradley, the former Seahawks defensive coordinator.
Trufant will help mentor a defensive backfield that includes five rookies.
The Jaguars drafted safety Johnathan Cyprien in the second round, cornerback Dwayne Gratz in the third and safety Josh Evans in the sixth. The team also selected cornerbacks Jeremy Harris and Demetrius McCray in the seventh round.