Chavez will join the Angels' spring training camp in Tempe, Arizona, after he clears their intake protocols, the team confirmed Friday.
Chavez appeared in 38 games for the Angels in 2017, making 21 starts. He left for Texas as a free agent after one season, and he excelled after being traded in July 2018 to the Chicago Cubs, where he was managed by current Angels skipper Joe Maddon.
Chavez, 37, spent the past two seasons back with the Rangers, struggling last season with a 6.88 ERA in 18 appearances.
With experience as a starter, long reliever and late-inning reliever, Chavez could provide versatility for the Angels, whose long-struggling pitching staff can use all the depth it can get.
Chavez is a native of the Los Angeles area, graduating from high school in Fontana before pitching in junior college in Riverside. He has also pitched for Pittsburgh, Atlanta, Kansas City, Toronto, Oakland and the Dodgers.