Arash Madani of Sportsnet first reported the deal. The Blue Jays will receive two prospects in the swap, right-handed pitcher Andrew Sopko and infielder Ronny Brito, while the Dodgers also get cash to cover part of Martin's salary, per The Athletic's Ken Rosenthal.
The four-time All-Star has one season left on his five-year, $82 million contract and is set to earn $20 million in 2019, per Spotrac.
The trade does not eliminate the Dodgers from the list of potential suitors for Miami Marlins standout catcher J.T. Realmuto, according to Fancred's Jon Heyman.
Martin, who's also made stops with the New York Yankees and Pittsburgh Pirates, is no longer the highly productive backstop he was during his first stint with Los Angeles. He posted a lackluster .225/.336/.399 triple-slash line with 66 home runs across four years with the Jays.
The 35-year-old former Gold Glove Award winner has also faded defensively. He ranked 15th among backstops in adjusted Fielding Runs Above Average in 2018, per Baseball Prospectus. He also finished 23rd in extra strikes earned per game via pitch framing, based on StatCorner analysis.
If the Dodgers aren't able to acquire Realmuto, Martin and Austin Barnes will likely split time pretty evenly behind the plate in 2019. It will be a weak spot in an otherwise strong L.A. lineup.
Meanwhile, Brito was rated as the Dodgers' No. 23 prospect by MLB.com before the trade. Sopko was unranked.
Brito, a 19-year-old shortstop, compiled an .855 OPS with 11 homers in 61 games across two stops in the lower minor leagues during the 2018 season.
Sopko, a 24-year-old starting pitcher, posted a 3.52 ERA with 121 strikeouts in 117.2 innings split between the Class-A Advanced and Double-A levels in 2018.