The club announced the move Tuesday.
Pierre, 32, hit .308 (117-380) with 30 stolen bases, 57 runs and a .365 on-base percentage in 145 games with the Dodgers in 2009.
Pierre is a career .301 hitter with 459 stolen bases, most among active players, and 804 runs scored in 1,433 games with Colorado (2000-02), Florida (2003-05), the Chicago Cubs (2006) and Dodgers (2007-09).
Pierre was on 2003 Florida Marlins team that won the World Series. White Sox manager Ozzie Guillen was the third base coach on that club.