The Angels announced the move Wednesday. They also designated left-hander Dillon Peters for assignment to clear a spot on the 40-man roster.
The White Sox designated Eaton for assignment July 7 after he batted .201 with five homers and 28 RBIs in 58 games in his return to Chicago. After a strong start to the year, his production slumped badly from mid-April onward.
The 10-year major-league veteran also struggled at the plate with the Washington Nationals in 2020, a year after playing well and winning a World Series ring with new Angels teammate Anthony Rendon.