"We had the opportunity to acquire one of the premier left-handers in the league over the last decade," new White Sox general manager Kenny Williams said.
Wells, 37, is 161-107 in a 14-year career and the White Sox will be his sixth team. He was 20-8 last season with a league-best nine complete games in 35 starts and has averaged 16 victories over the last six years.
Wells has been at his best in the postseason with an 8-1 record in 19 games.
Earlier this month, Wells said the Blue Jays were not doing enough to win. He also said the Blue Jays' fans "stink."
"They are terrible," he said before leaving for his honeymoon in New Zealand.
There had been speculation that Wells might wind up back in New York, this time with the Mets in a deal, possibly for outfielder Jay Payton and pitcher Glendon Rusch.
Sirotka went 15-10 last season for Chicago. He is 45-42 overall in 125 major league games.
Wells, known for his girth, personality and love of a good time, is signed through the 2001 season.
Nicknamed "Boomer," the outspoken and popular pitcher worked 229 2-3 innings last season and allowed an AL-low 1.2 walks per nine innings.
Wells pitched a perfect game for the Yankees on May 17, 1998, against Minnesota. He helped lead the Yankees to the World Series championship later that season, but then was traded to Toronto for Roger Clemens in a deal during 1999 spring training.
Wells also has pitched for Detroit, Baltimore and Cincinnati.
Sirotka, 29, made 32 starts last season and was considered the White Sox ace as they made the playoffs for the first time since 1993.
"It was extremely tough to depart with a quality pitcher and person like Mike Sirotka," Williams said after making his first major trade.
DeWitt, 23, was 1-0 in eight outings for the Blue Jays last season. He spent most of the season with Triple-A Syracuse, where he was 4-5 record.
Beirne, 27, was mainly a reliever for the White Sox. He was 1-3 wth a 6.70 ERA in 29 games. Simmons, 27, missed the entire season after rupturing his Achilles' tendon in spring training. Williams, 22, was 3-4 at Class A Winston-Salem.
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