Toronto gave up pitching prospect Nestor Molina to acquire the 28-year-old Santos in a swap made at baseball's winter meetings.
Santos had 30 saves in 36 chances this year, going 4-5 with a 3.55 ERA in 63 games. The 28-year-old righty is a strikeout pitcher, fanning 92 in 65 1-3 innings. He made a major league-record 25 straight scoreless appearances on the road to start the season.
Santos was golfing when Toronto general manager Alex Anthopoulos called to tell him about the trade. The deal caught Santos by surprise — a few days after the season ended, he signed an $8.25-million, three-year contract with the White Sox.
"I think he expected to be in Chicago," Anthopoulos said.
Santos was in Toronto's minor league system from 2006-08 as a shortstop. He converted to pitching in 2009 while in the White Sox organization and made his big league debut the next year.
Anthopoulos was the Blue Jays' assistant GM when Santos was in their organization. The team asked Santos if he wanted to take a try on the mound, but he wasn't interested.
"He didn't want to pitch. He believed in himself as a shortstop," Anthopoulos said.
Santos made it as high as Triple-A as an infielder. He was a career .248 hitter with 72 home runs in the minors, starting out in 2002 in the Arizona system.
The Blue Jays really wanted him back and were willing to trade Molina. The 22-year-old starter has excelled in his minor league career, going 27-7 with a 2.21 ERA overall. He was a combined 12-3 with a 2.21 ERA in Double-A and Class A last season.
Anthopoulos said Santos' contract situation and "electric stuff" made him especially attractive, given his arm hasn't endured a lot of wear because of his late switch to pitching.
Toronto's saves leader last season was Frank Francisco with 17. Santos immediately inherited the role.
"He's got the ninth inning for us," Anthopoulos said. "We think he's got a chance to be an elite closer."
Chris Sale was second on the White Sox last season with eight saves. Chicago had planned to move him into the rotation next year.
Asked who would be the Chicago closer in 2012, new manager Robin Ventura wasn't sure.
"I knew yesterday," he said. "But obviously, you know, right now you're going to wait and see how the rest of this week goes and figure it out from there."