"Zach Stewart has been on our radar for a long time, especially last year, when he was doing special things in Double A," Chisox General Manager Ken Williams told the Chicago Tribune. "As for Jason Frasor, he's one of the top-quality relievers in baseball ... .
"Edwin Jackson and Mark Teahen are consummate professionals, but we needed to make a little bit of a dent in our payroll. We didn't want to do anything that would be counter-productive to winning."
The transaction will save the White Sox about $9 million over the next 18 months.
The teams agreed on the players in the trade Tuesday afternoon, and Major League Baseball approved it late Tuesday night.
Frasor, 33, is 2-1 this season with a 2.98 ERA as a reliever.
Stewart, 24, has pitched in three games for the Blue Jays this season and is 0-1 with a 4.86 ERA. He will report to Class AAA Charlotte, but Williams said he will be ready for the majors soon.