Terms of the deals were not disclosed.
In addition, the team released linebacker Chaz Sutton and offensive lineman Tevita Stevens from its practice squad.
Cave (6-3, 305) originally signed with the Cleveland Browns as a college free agent on April 30, 2013. He was waived by the Browns on Aug. 30, 2013, and then signed with the New England Patriots on Sept. 1, 2013.
Cave spent the 2013 season on the Patriots’ practice squad and spent the 2014 offseason with the team before being waived on Aug. 30.
Cave played collegiately at Notre Dame, where he appeared in 48 games with 35 starts. He was named a third-team All-American by the Associated Press during his final season in 2012.
Cave, 25, attended Penn H.S. in Mishawaka, Ind., where he helped lead his school to an undefeated regular season his senior year. He was born on July 29, 1989.
Jeffcoat (6-3, 253) originally signed with the Seattle Seahawks as a college free agent on May 10, 2014, before being waived by the team on Aug. 25.
Jeffcoat, 22, played collegiately at Texas, where he appeared in 40 games with 33 starts. During his senior season, he led his team with 86 tackles, 22 tackles for loss, 13 sacks, and 19 quarterback pressures. He was a consensus All-American, in addition to capturing the Ted Hendricks Award as the nation’s top defensive end, following in the footsteps of fellow Redskins linebacker
Jeffcoat attended Plano West H.S. in Plano, Texas, where he was named a prep All-American, two-time first-team all-state and all-area selection and a three-time all-district defensive end. He was born on Dec. 26, 1991.