He has previously played in Major League Baseball (MLB) for the New York Yankees, Detroit Tigers, Atlanta Braves, Los Angeles Dodgers, and Chicago Cubs.

Greene attended East Ridge High School in Clermont, Florida, and played for their baseball team as a pitcher.

On June 12, Greene was optioned to the Toledo Mud Hens of the International League, and his spot in the rotation was given to Kyle Ryan.

After returning to the Tigers following a stint with the Toledo Mud Hens on July 12, he gave up 17 runs on 24 hits over 132⁄3 innings.

[19] Greene made the Tigers' 2016 starting rotation, though he pitched out of the bullpen in the team's April 5 opening day game against the Miami Marlins and earned his first major league save.

[20] After pitching three innings of an April 24 start against the Cleveland Indians, Greene was removed from the game due to a blister on his throwing hand, and was placed on the 15-day disabled list.

[21] For the 2016 season, Greene made 50 appearances (47 in relief), posting a 5–4 record and 5.82 ERA, while striking out 59 batters in 60+1⁄3 innings pitched.

[27] Greene finished April with 12 saves, 17 strikeouts, three walks and a 1.29 ERA in 14 appearances, and won American League Reliever of the Month honors.

[29] In the All-Star Game, Greene earned a hold by pitching a clean seventh inning, retiring all three batters he faced.

[30] On July 31, 2019, the Tigers traded Greene to the Atlanta Braves in exchange for Joey Wentz and Travis Demeritte.

[31] Greene was acquired by the Braves to fill a closer role that had previously been held by Arodys Vizcaíno, A. J. Minter and Luke Jackson.

[32] Due to initial struggles by Greene, Braves manager Brian Snitker removed him from the closer's role on August 9 and promoted Mark Melancon to that position.

On May 9, 2021, Greene re-signed with the Braves on a one-year, $1.5 million contract, and was assigned to the Triple-A Gwinnett Stripers to get back into game shape.

[42] He pitched 6+2⁄3 innings over nine games for the Dodgers and allowed three runs on three hits and five walks before he was designated for assignment on September 22.

On October 23, 2021, Greene debuted with Cardenales de Lara in the Venezuelan Professional Baseball League (LVBP).

[44][45] On March 16, 2022, Greene signed a one year minor league deal to stay with the Dodgers organization [46] and was added back to the 40-man roster on May 15.