Soto was sent to Texas for minor league pitcher Jake Brigham and a player to be named later or cash considerations, the teams said.
Soto, who was drafted by the Cubs in 2001 and has played his entire major league career in Chicago, is hitting .199 with six home runs and 14 runs batted in in 52 games this season.
The 29-year-old is four years removed from his best offensive season. He hit .285 with 23 home runs and 86 RBI in 2008 when he was voted the National League Rookie of the Year.
Over his career, Soto is a .252 hitter with 77 home runs and 264 RBI.
Brigham, a 24-year-old right-hander, is 5-5 with a 4.26 earned run average in 21 starts at Double-A Frisco this season.
To make room for Soto on the roster, the Rangers designated catcher Yorvit Torrealba for assignment. He is hitting .236 with three home runs and 12 RBI in 49 games.