The 25-year-old right-hander missed nearly the whole season after back surgery. He pitched in just one game for the Dodgers in 2013, walking both batters he faced on April 12 in Arizona. He went on the disabled list shortly after that and never pitched again this season.
Tolleson has one year, 122 days of service time and two option years remaining.
In a matter of days the Dodgers lost their 2013 ERA leader in Skip Schumaker (who pitched two scoreless innings) and now their pitcher with an infinite WHIP, as Tolleson didn't record an out this season.
Tolleson had a 4.30 ERA in 40 games in relief in 2012, with 39 strikeouts and 20 walks in 37⅔ innings. With the Rangers, Tolleson returns to his home state, having pitched at Allen High School in Allen, Texas and for Baylor University in Waco.
With the move the Dodgers have 31 players on the 40-man roster, though that will increase this evening when rosters are set in preparation of the Rule 5 Draft.