Tate played with the Browns, Vikings and Steelers last season, while Jones previously played with the Cowboys.
Tate played with three teams last season, while Jones has not played since the 2013 season, when he was with the Steelers.
Dallas' backfield remains in a state of flux after starter DeMarco Murray signed with divisional rival Philadelphia this off-season. The team added veteran Darren McFadden on a two-year deal and returns Lance Dunbar and Joseph Randle. The Cowboys also signed former Cardinals running back Ryan Williams off the practice squad.
Tate began last season with the Cleveland Browns, for whom he appeared in eight games before being released after his playing time dwindled in a three-back committee system. He signed a two-year, $6.2 million deal last off-season to play for Cleveland.
Jones previously played with the Cowboys from 2008-12, rushing for a cumulative 2,728 yards and 11 touchdowns. In 2013, he rushed for 184 yards on 48 attempts for the Steelers.
Entering his sixth NFL season out of Auburn, Tate holds a career average of 4.4 yards per carry and has run for 14 touchdowns.
- Jeremy Woo