In addition, the Cowboys cut defensive tackle Cedric Thornton, their biggest free-agent signing in 2016, according to ESPN. Thornton signed a four-year, $17 million deal that included $9 million guaranteed, but he did not become a starter and was slowed in training camp by a hamstring strain.
Dallas gave up a 2018 seventh-round conditional draft pick to acquire Elliott, the Dallas Morning News reported.
The Cowboys were awarded defensive tackle Brian Price off waivers from the Packers, according to ESPN.
The Cowboys needed depth at linebacker with Anthony Hitchens out eight weeks with a tibial plateau fracture in his right knee and Jaylon Smith still limited as he recovers from his major left knee injury that kept him out all of his rookie season.
The 6-foot-3, 255-pound Elliott re-signed with the Packers to a one-year deal worth $1.6 million that included a $350,000 signing bonus. In 11 games last season, he led the Packers with 13 special teams tackles and was credited with 19 on defense with one sack.
Elliott, 25, was entering his fourth season with the Packers. He played in 38 games (no starts) over the last three seasons with the Packers and had a total of 57 tackles and four career sacks. He went undrafted in 2014 out of Toledo.
The 6-foot-4, 290-pound Thornton, 29, played in 13 games for the Cowboys in 2016 and made 22 tackles and 1.5 sacks.
The 6-3, 218-pound Price, 23, played in just one game last season for the Packers and spent time on the practice squad.