Smith, 27, joined the Cowboys in 2015 and has served as a back-up to workhorse running back Ezekiel Elliott for the majority of his four-year NFL career. He entered the league as an undrafted free agent out of Ohio State.
Smith is now expected to compete for a back-up role behind Giants star running back Saquon Barkley.
Smith visited the Cincinnati Bengals before signing with the Giants. The 6-foot-3, 235-pound ball-carrier had 127 yards and a touchdown on 44 carries in 16 games last season. Smith started in the Cowboys' regular-season finale against the Giants, rushing for 35 yards and a touchdown on 12 carries in a 36-35 victory.
He had his best season in 2017, piling up 434 yards from scrimmage and five touchdowns on 74 touches in 15 games for the Cowboys.
If Smith makes the team, he'll face his former team in Week 1 of the 2019 season. The Cowboys host the Giants at 4:25 p.m. on Sept. 8 at AT&T Stadium in Arlington, Texas.