Green did not attend college, and was signed by the Kansas City Athletics before the 1960 season as an amateur free agent. Green spent a few seasons in the minor leagues before being called up on September 9, 1963. Green played minimally in 13 games, but did pick up 10 hits, including his first major league home run.
In 1966, Green improved, hitting .250, slapping in 127 hits in 140 games, and also knocked in 62 runs. However, Green struggled the following season. With 69 hits in 122 games, Green coupled his .198 batting average with 5 home runs and 37 RBIs.
Green was a member of the 1972-1974 World Series championship Oakland Athletics team, and won the Babe Ruth Award for his performance in the 1974 World Series. Green won the award for his fielding, despite not getting a single hit during the World Series. Green tied a World Series record in game three by starting three double plays in one game. He started the first two by catching line drives, and the third was a ground ball double play to end the game. In game four, Green also started a game ending double play. In the eighth inning of the clinching game five, Green made a perfect relay throw to get Bill Buckner, representing the tying run, out at third base. Overall for the six double plays Green participated in during 1974 World Series tied the record for most defensive double plays in a five game series.