Earlier this week, the White Sox unconditionally released Eaton, who was in his second stint with the club after signing a one-year, $8 million contract that included a team option for 2022.
The 32-year-old Eaton was batting .201 with five home runs, 28 RBIs and 33 runs scored over 58 games for the White Sox this season. Chicago released him Monday.
The left-handed Eaton, who was designated for assignment July 7, spent the past four seasons with the Nationals (2017-20) before joining the White Sox in the 2021 campaign. He also has played for the Arizona Diamondbacks during his 10 MLB seasons.
Eaton played his first two seasons in Arizona (2012-13) before his first stint in Chicago (2014-16).
Eaton, who led the American League in triples in 2014 and 2016, has a .278 batting average with 65 home runs and 317 RBIs in 889 career games.
To make room for Eaton on the 40-man roster, the Angels designated left-hander Dillon Peters for assignment.