The Red Sox acquired Horn from the White Sox on Tuesday in exchange for cash, Chris Cotillo of The Springfield Republican reports.
Horn was designated for assignment by the White Sox on Friday, Daryl Van Schouwen of the Chicago Sun-Times reports.
The White Sox optioned Horn to Triple-A Charlotte on Tuesday.
Horn was acquired by the White Sox from the Cubs on Tuesday in exchange for Matthew Thompson, Ken Rosenthal and Sahadev Sharma of The Athletic report.
The Cubs selected Horn to their 40-man roster Tuesday, Andy Martinez of Marquee Sports Network reports.
Horn was reassigned to minor-league camp Saturday, Meghan Montemurro of the Chicago Tribune reports.