The team announced the trade Saturday afternoon, a day after placing veteran right-hander Clay Buchholz on the 10-day injured list with shoulder inflammation.
Buchholz was the latest Blue Jays starter to go down with injury. Right-hander Matt Shoemaker tore his ACL last month and is out for the season, while left-handers Clayton Richard and Ryan Borucki are also on the injured list and have yet to appear in a major league game in 2019.
Jackson made 17 starts for the Athletics last season, going 6-3 with a 3.33 earned-run average. He had been pitching in triple-A before the trade.
Blue Jays manager Charlie Montoyo said Jackson could start as early as Wednesday against the San Francisco Giants.
"Hopefully he gives us a spark. I’ve seen him for a long time now so hopefully, he helps us out," Montoyo said.
The 35-year-old has posted a 104-123 record with a 4.60 ERA in 1,892 1/3 career innings at the major league level.
Toronto had been relying primarily on a four-man rotation since Shoemaker’s injury on April 20. The Blue Jays used reliever Daniel Hudson as an opener Friday against the Chicago White Sox in place of Buchholz.
Jackson’s trade to Toronto will make him a new MLB record holder. In 2018 he matched Octavio Dotel by pitching with his 13th big league team.
Jackson broke in with the Los Angeles Dodgers in 2003 and pitched for Tampa Bay, Detroit, the White Sox, Arizona, St. Louis, Washington, the Cubs, Atlanta, San Diego, Miami and Baltimore.