The 32-year old Peavy was 8-4 with a 4.28 ERA for Chicago this season. The right-hander is a former Cy Young Award winner and three-time All-Star.
Boston sent a trio of minor leaguers to the White Sox in the deal.
The Red Sox acquired reliever Brayan Villarreal from Detroit and sent shortstop Jose Inglesias to the Tigers. Boston also got outfielder Avisail Garcia from Detroit and sent him to the White Sox.
In other major league trades;
– The Oakland Athletics have acquired third baseman Alberto Callaspo from the Angels for infielder Grant Green. Callaspo is hitting .253 with five home runs and 36 RBIs entering Tuesday. Green is hitless in 15 at-bats during his first stint in the major leagues this season.
– The Cleveland Indians have acquired left-handed reliever Marc Rzepczynski from the St. Louis Cardinals. The Indians sent minor league infielder Juan Herrera to St. Louis.