Jackson, 35, impressed in spring training but was granted his release last Thursday when Toronto didn’t add him to the roster.
The right-handed journeyman will now return to the team on a split contract and will begin the season in triple-A Buffalo.
Over 9.1 innings of Grapefruit League action with the Blue Jays, Jackson allowed no earned runs and struck out 13 hitters while walking only two.
To make room for Jackson on the 40-man roster, Toronto officially placed off-season acquisition Green on the injured list as he recovers from Tommy John surgery.
Green signed with the Blue Jays for two years and $8.5 million in a complex contract that includes multiple options.
In six years with the New York Yankees, the right-hander has a 3.17 ERA and 494 strikeouts over 383.2 innings.
Toronto kicks off the regular season on Thursday in St. Louis against the Cardinals. The game can be seen on Sportsnet and SN NOW, starting at 4 p.m. ET / 1 p.m. PT.