Chicago dealt right-hander Jeff Soptic, a 2011 third-rounder, for the 37th overall selection in the 2008.
White Sox general manager Rick Hahn told MLB.com that Gillaspie will have every chance to prove himself at Spring Training and make the team.
"He conceivably fits in nicely on the roster, which we'll obviously decide more about toward the end of next month," Hahn said. "But we see him having a solid hit tool, above-average awareness of the strike zone, [he's] solid defensively. He gives us a little versatility in his ability to play third base as well as first. He gives [manager Robin Ventura] some options, potentially."
"You bring him in and see how he competes, really, and it opens up options," Ventura added.
Gillaspie, who becomes the White Sox No. 15 prospect, spent last season with Triple-A Fresno in his second tour of the Pacific Coast League. He hit .281/.345/.441 with 14 homers and 49 RBIs in 108 games to follow up a 2011 campaign in which he batted .297/.389/.453 with 11 homers and 61 RBIs in 124 games.
The 25-year-old had three brief stints with San Francisco since 2008, hitting .205 in 29 games.
Soptic, a 21-year-old out of Johnson County Community College in Kansas, went 3-2 with a 5.40 ERA in 27 appearances out of the bullpen for Class A Kannapolis last season. Over 43 1/3 innings, he struck out 36 batters and walked 29. The 6-foot-6 right-hander reportedly works in the mid-90s, occasionally touching 98 or 99 mph, and can throw a slider, sinker and change.
Bobby Evans, the Giants' vice president of baseball operations, told MLB.com that Soptic will likely begin the year at Class A Advanced San Jose.