[5][6] He left as the school record holder in career earned run average (ERA), at 2.38.

On December 9, 2015, the Tigers traded Green and Luis Cessa to the New York Yankees for Justin Wilson.

After four starts, the Yankees shut down Green for the season when he suffered a sprained elbow ligament.

[17] Instead of naming a fifth starter, the Yankees optioned him to the minors and carried an extra reliever instead.

[26] He made his return on May 12, recording three strikeouts in the ninth inning to close out a 7–1 win against Tampa Bay Rays.

[28] After throwing 4+2⁄3 scoreless innings in the playoffs, he allowed a three-run homer to Carlos Correa of the Houston Astros in Game 4 of the 2019 ALCS.

[29] He was the team's opener in Game 5, allowing a three-run home run to Yuri Gurriel in the first inning.

[35] However, Green exited the Yankees' May 19 game against the Orioles due to right forearm discomfort.

[36] Three days later, the team confirmed that Green would undergo Tommy John surgery, ending his season.

[37] On January 31, 2023, Green signed a two-year, $8.5 million deal with the Toronto Blue Jays.

Given that he was still recovering from Tommy John surgery at the time, the deal has a unique structure.

[38][39][40] He was activated from the injured list on September 1, and made his Blue Jays debut on that same day.