- Bats Right, Throws Right
- Height 6' 4", Weight 210 lb.
- School University of West Florida, Daytona Beach Community College
- High School East Ridge High School
- Debut April 24, 2014
Greene was undrafted out of high school. He went to the University of West Florida on scholarship, but blew out his elbow late in his freshman season. After Tommy John surgery, he lost his scholarship and transfrred to Daytona Beach Community College. He was drafted by the Yankees in the 15th round of the 2009 amateur draft and began his professional career that year..
Pitching for the GCL Yankees, he was 1-2 with a 5.87 ERA in 13 relief appearances in his rookie season. After converting to starting pitching for 2010, he went 2-8 with a 4.59 ERA in 14 starts for the Staten Island Yankees (2-6, 4.59) and Charleston RiverDogs (0-2, 4.58). In 2011, the hurler was 5-14 with a 4.37 ERA in 27 starts for Charleston. He led the South Atlantic League in losses (two more than runner-up Jarret Martin), tied for 5th in runs allowed (88), was 5th in walks (68), was 4th in strikeouts (128, behind Garett Claypool, Spencer Arroyo and Roman Mendez) and tied for 10th with 14 wild pitches. Among Yankee farmhands, he had the most defeats (two more than Jose Ramirez), tied for second in runs allowed with Craig Heyer, was 4th in walks (between Dellin Betances and D.J. Mitchell), was second in strikeouts (14 behind Betances), tied Heyer and Betances for third in hit batsmen (10) and tied for 7th in wild pitches. He tied for 5th in the minor leagues in losses, behind only Edgar Olmos, J.R. Bradley, Wilfredo Boscan and Chad James.
In 2012, he was 4-7 with a 5.22 ERA in 24 games (23 starts) for the Tampa Yankees, walking 63 in 112 IP. He tied Perci Garner and Eliazer Suero for third in the Florida State League in walks. Among Yankee farmhands, he was 4th in that department, between Bryan Mitchell and Brett Marshall. He went 12-10 with a 3.38 ERA in 27 games (26 starts) split between Tampa (4-6, 3.60 ERA, 13 starts) and the Trenton Thunder (8-4, 3.18) in 2013. His control was much sharper, with 30 walks in 154 1/3 IP and only 10 homers allowed. He led Yankee minor leaguers in wins, one ahead of Nik Turley and Scottie Allen, tied Marshall and Mikey O'Brien for third in losses, allowed the most hits (175, 17 ahead of Bryan Mitchell) and was third in Ks (behind De Paula and Turley). His performance with Tampa earned him a spot in the Florida State League All-Star Game, while MinorLeagueBaseball.com named him an Organization All-Star following the season. Greene was added to the Yankees 40-man roster following the season.
He was in a notable spring training game in 2014 because it was against Florida State University and Heisman Trophy winner Jameis Winston. Greene retired Winston on a grounder. He started the season in the minors but saw little action with the Scranton/Wilkes-Barre Yankees (4 H, 1 BB, 2 R, 5 K in 2 2/3 IP). With Michael Pineda suspended, the Yankees called up Bruce Billings and Greene for arm reinforcement, sending down Dean Anna and Preston Claiborne to open roster space. He made his major league debut on April 24th when he gave up 3 unearned runs on 3 walks in a third of an inning against the Boston Red Sox. He came into the game in the 7th with the Yanks leading, 12-2, but walked Jackie Bradley and allowed Dustin Pedroia to reach on an error. A passed ball scored Bradley from third base and he then struck out Shane Victorino. He walked pinch-hitter Jonathan Herrera and Mike Napoli to load the bases, at which point he was replaced by Adam Warren; two more runs scored on a sacrifice fly and a double by Xander Bogaerts before the inning ended. After the one outing in the majors, he was sent down in favor of Chris Leroux. He only came back to the big leagues on July 7th, when he started against the Cleveland Indians in place of Vidal Nuno, who had been traded the day before. Things went much better this time, as he kept the Indians hitless until the 5th inning, when Nick Swisher touched him for a solo homer; he left after allowing 2 runs in 6 innings and was credited with his first major league win, 5-3. He ended up making 14 starts in 15 appearances for New York, with a record of 5-4, 3.78 and 81 strikeouts in 78 2/3 innings.
On December 5, 2014, Greene was involved in a three-team trade that allowed the Yankees to acquire the heir apparent to SS Derek Jeter as they landed Didi Gregorius from the Arizona Diamondbacks. For his part, Greene was immediately flipped to the Detroit Tigers in return for two prospects, P Robbie Ray and IF Domingo Leyba. He was a winner in his first start for Detroit on April 9, 2015, 7-1 over the Minnesota Twins. By only allowing an unearned run in the 7th inning, he extended the Tigers' streak of scoreless innings since the start of the season to an American League-record 24. His second start on April 14th was just as solid, as this time he allowed no runs in 8 innings in defeating the Pittsburgh Pirates, 2-0. His run of good pitching ended on April 24th, when he allowed 8 runs in 4 innings in a 13-1 loss to the Cleveland Indians. He all tumbled down from there as he ended up going 4-8, 6.88 in 18 games, 16 of them starts. In 2016, he was moved to the bullpen, making 50 appearances but just 3 starts in going 5-4, 5.82, with the first 2 saves of his career.
He emerged as a front-line reliever in 2017 when he pitch 71 times, all in relief, logging 67 2/3 innings with an ERA of 2.66 and 73 strikeouts. His record was 4-3 and he recorded 9 saves. By 2018, he had been promoted to full-time closer for the Tigers and recorded 32 saves with a 4-6 record, but his ERA shot up to 5.12, as his hit rate was over 1 per inning for the first time since his days as a starter. He turned that around in the first half of 2019, as he became the Tigers' sole representative at the All-Star Game after going 0-2 but with a 1.18 ERA and 22 saves in 32 games. This was achieved with a last-place team, so it made him an inviting target at the trading deadline. On July 31st, he was sent to the Atlanta Braves in return for Travis Demeritte and Joey Wentz. He was back to a set-up role with the Braves, saving just 1 game in 27 outings with an ERA of 4.01. His combined pitching line was 0-3, 2.30 in 65 games, with 64 strikeouts in 62 2/3 innings. He appeared in the postseason for the first time that year with 2 games in the Braves' loss to the St. Louis Cardinals in the Division Series; he gave up 1 run on 4 hits in 2 2/3 innings.
Greene was back with the Braves during the pandemic-shortened 2020 season, working again as a set-up man. He made 28 appearances and his only decision was a win. He allowed 22 hits against 21 strikeouts in 27 2/3 innings. This time, the Braves made a deeper postseason run and he made 6 appearances, including 4 in the NLCS against the Los Angeles Dodgers. He did quite well, allowing just 1 run in 6 innings of work, with 6 strikeouts and just 1 walk. He became a free agent after the season but surprisingly, given his rather good record over recent years, he did not sign with anyone before spring training. He was still a free agent at the beginning of May 2021, when the Braves finally inked him to a one-year deal on May 9th, although given his lack of recent work, he first needed to head to AAA with the Gwinnett Stripers to work himself back into game shape.
- AL All-Star (2019)
- 30 Saves Seasons: 1 (2018)