Greene attended Paul J. Hagerty High School in Oviedo, Florida, where he played on their baseball team alongside Vaughn Grissom.

[7][8] Greene made his professional debut on June 24, 2019, for the rookie-level Gulf Coast League Tigers.

[15] Over 124 games between the two clubs, Greene slashed .301/.387/.534 with 24 home runs, 84 RBIs, 16 stolen bases, 25 doubles, and eight triples.

[18][19] On June 18, 2022, the Tigers purchased Greene's contract, adding him to the active roster, and he made his Major League debut that afternoon.

[25] The next day, the Tigers announced that Greene had undergone Tommy John surgery, and would likely be ready by the start of the 2024 season.

[28] For the season, Greene hit .262/.348/.479 with 24 home runs and 74 RBIs in 137 games, as he helped the Tigers return to the playoffs after a 10-year drought.