The Cubs traded Thaiss to the White Sox on Tuesday in exchange for cash, Andy Martinez of Marquee Sports Network reports.
The Cubs acquired Thaiss from the Angels on Wednesday in exchange for cash consideration, Jesse Rogers of ESPN.com reports.
The Angels designated Thaiss for assignment Thursday, Bill Shaikin of the Los Angeles Times reports.
Thaiss is absent from Saturday's lineup against Texas, Jeff Fletcher of The Orange County Register reports.
Thaiss will start at catcher and bat sixth in Wednesday's game against the White Sox, Erica Weston of Bally Sports West reports.
Thaiss went 2-for-3 with a solo home run in Wednesday's loss to the Blue Jays.
Thaiss went 2-for-2 with three walks and a stolen base in a 6-4 win over Washington on Sunday.
Thaiss will start at catcher and bat eighth in Wednesday's game against the Mariners.
Thaiss will start at catcher and bat ninth in Wednesday's game against the Athletics.
Thaiss went 1-for-2 with a two-run home run in Sunday's loss to Cleveland.