Beckham has struggled offensively this year, but he gives the AL West-leading Angels another sure-handed infielder with six seasons of major league experience. He turns 28 on Sept. 16.
The White Sox, who selected Beckham with the eighth overall pick in the 2008 draft, will receive a player to be named or cash in Thursday's trade.
Beckham made his major league debut in 2009 and hit .270 with 14 homers and 63 RBIs in 103 games with the White Sox. But he is batting .221 this year with seven homers and 36 RBIs in 101 games. He also has a .981 fielding percentage.
The White Sox will make a corresponding roster move before Friday night's game at the New York Yankees.