Eaton, 32, was in his second stint with the White Sox after signing a one-year, $8 million deal that included a team option for 2022. He was batting .201/.298/.344/.642 with five homers, 28 RBIs and 33 runs scored over 58 games this season.
The left-handed Eaton, who was designed for assignment last Wednesday, has also played for the Washington Nationals and Arizona Diamondbacks during his 10 MLB seasons. He has a career .278 batting average with 65 home runs and 317 RBIs.
Eaton will provide immediate depth in the Angels' injury-plagued outfield. Left fielder Justin Upton has been out since June 22 with a lower back injury, and three-time AL MVP center fielder Mike Trout has been out for two months with a left calf injury. Both should return relatively soon, but their injuries have been slow to heal, preventing them from even starting a rehab assignment before the All-Star break.
Los Angeles also lost right fielder Dexter Fowler for the season with a torn knee ligament in early April.
The Angels have been using infielders Luis Rengifo, Jose Rojas and Phil Gosselin as fill-in outfielders while Upton and Trout have been out. Juan Lagares, who is usually filling in for Trout in center field, and Taylor Ward were the only true healthy outfielders on the Halos' roster for most of the past three weeks.
The Angels are still playing well offensively despite their significant injury problems and Rendon's season-long slump. They rank eighth in the majors in runs (435) and fifth in team OPS (.759) behind All-Star sluggers Shohei Ohtani and Jared Walsh.
The Associated Press contributed to this report.