The Giants signed Stassi (hip) to a minor-league contract Nov. 19.
The White Sox declined Stassi's $7.5 million club option for 2025 on Friday.
The White Sox announced that Stassi underwent a season-ending left hip surfacing procedure Friday in New York City.
Stassi (hip) was transferred to the 60-day injured list by the White Sox on Monday.
Stassi (hip) reported to Triple-A Charlotte on Tuesday to begin a rehab assignment, Vinnie Duber of AllCHGO.com reports.
The White Sox placed Stassi on the 10-day injured list Monday with left hip inflammation, James Fegan of SoxMachine.com reports.
White Sox manager Pedro Grifol said Sunday that Stassi's availability for Opening Day is up in the air due to unspecified soreness, Daryl Van Schouwen of the Chicago Sun-Times reports.
Atlanta traded Stassi (hip/personal) and cash considerations to the White Sox on Saturday in exchange for a player to be named later or cash.
The Angels placed Stassi (personal) on the restricted list Sunday.
Angels manager Phil Nevin told reporters Saturday that Stassi (personal/hip) remains without a timetable, but he has resumed participating in baseball activities and working out, Rhett Bollinger of MLB.com reports.