The club also announced that reliever Nick Kingham has been assigned to triple-A Buffalo after clearing waivers.
Jackson, 35, was designated for assignment after posting a 1-5 record with an 11.12 earned-run average in eight games this season. The Blue Jays acquired the right-hander from the Oakland Athletics for cash considerations back in May to provide some depth in the starting rotation.
Kingham appeared in 10 games for Toronto after being acquired from the Pittsburgh Pirates in June for cash considerations. The 27-year-old had a 2-1 record with a 3.50 earned-run average in 18 innings.