This move was one of two the Blue Jays made near the end of the non-waiver trade deadline. They also acquired Houston Astros pitcher Scott Feldman.
Chavez, 32, posted a 4.57 ERA with 42 strikeouts to 10 walks in 39 relief appearances for the Blue Jays this season.
Bolsinger, 28, began his career as a starter but transitioned into a reliever this season down in the minors. In six starts with Los Angeles this season Bolsinger has posted a 6.83 ERA.