Heading back Toronto’s way will be right-handed pitching prospect Corey Copping.
Axford, a free agent after the season, will help the Dodgers as they attempt to hold off the Arizona Diamondbacks in the NL West.
The 35-year-old sports a 4.41 ERA with 50 strikeouts and 20 walks in 51 innings pitched spread across 45 games played with the Blue Jays this season.
Copping, 24, has a 2.52 ERA and boasts a K/9 of 9.9 combined between double-A and triple-A this season.
The Blue Jays have been busy in the relief market, sending Aaron Loup to Philadelphia and Seunghwan Oh to Colorado.