Dallas shipped a sixth-round selection (No. 192 overall) in exchange for Austin, who never could find a role last season in first-year head coach Sean McVay's offense.
The Cowboys were in need of help at wideout after releasing Dez Bryant earlier this month.
Austin was limited to a career-worst 13 receptions for 47 yards last season for the NFC West champion Rams, although he did finish second on the team in rushing with 270 yards and a touchdown on 59 carries.
The No. 8 overall selection in the 2013 NFL Draft out of West Virginia, Austin established a career high with 58 receptions for 509 yards in 2016.
The 5-foot-8, 180-pound Austin never developed into the deep threat envisioned by the Rams, but he did have 52 catches for four touchdowns while adding 434 yards rushing and five more scores on the ground in 2015.
Austin also is a weapon in the return game, taking back three punts for touchdowns in his career.
The trade gave the Rams seven selections in the sixth round.