Torrealba is hitting .236 with three home runs and 12 RBIs in 49 games with a .302 on-base percentage and a .342 slugging percentage. The Rangers were also unhappy with his defense and were looking for an upgrade behind Mike Napoli.
Soto has been a front-line catcher with some power until this season. The Rangers are hoping he can step it up after being traded to a new team and finding himself in the middle of a pennant race.
"We're excited to add Geovany to our club," general manager Jon Daniels said in a statement. "He's a talented guy we think can contribute to what we're hoping to accomplish. We also want to thank Yorvit for his work here over the past two seasons."
The Cubs will also receive a player to be named later or cash considerations from the deal.
Soto, who won the National League Rookie of the Year Award and was named an All-Star in 2008, is hitting a career-worst .195 with six home runs and 14 RBIs in 51 games. But he has had his best month of the season in July, hitting .250 with one home run, five RBIs and eight runs scored.
Soto was sidelined from May 17 to June 17 after undergoing surgery to repair a torn meniscus in his left knee. He had a pair of multi-hit games and two home runs in the first three games he played after being activated from the disabled list on June 18. Since coming off the DL, Soto is hitting .241 with three home runs and eight RBIs in 24 games and 83 at-bats.
Soto is a career .252 hitter with 77 home runs, 264 RBIs and a .445 slugging percentage in 554 games since his Major League debut in 2005.
Soto, who is from Puerto Rico, is making $4.3 million this season and can't be a free agent until after the 2013 season. He is eligible for arbitration this winter. With Napoli being a free agent at the end of the season, Soto could potentially give the Rangers an experienced option at catcher for 2013.
Brigham was on the Rangers' 40-man roster, but he is not among their Top 20 Minor League prospects. In 21 starts with Frisco, Brigham is 5-5 with a 4.28 ERA, 116 strikeouts and 46 walks in 124 innings. He was the Rangers' sixth-round pick in the 2006 First-Year Player Draft. A Texas League All-Star this year, Brigham tossed six shutout innings in his last outing Saturday and is 1-0 with a 2.00 ERA in his last three starts.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.