The White Sox announced the move before Wednesday night’s game against Detroit.
The 24-year-old Alvarez was part of the relay team at the Sochi Olympics that won the silver medal in the 5,000-meter relay.
Alvarez was a standout shortstop in high school in Miami. He missed making the Olympic skating team in 2010 and then played for Salt Lake Community College in Utah in 2011, batting .303 with 43 RBIs.
Alvarez will soon begin working out in Arizona.