Greene was drafted by the Angels in 1993 and bashed 40 homers between Double-A and Triple-A in 1995 to attain top-prospect status. Despite his dreadful fielding stats (44 passed balls in 1994), Anaheim tried their best to get his bat into the lineup in 1996. Unfortunately, elbow and shoulder injuries curtailed his production and limited him to DH duties for three years.
The Angels finally cast Greene aside in the spring of 2000 and he spent an uneventful year with the Blue Jays before signing with the Yankees. Greene caught for Triple-A Columbus until June 2001, when he was called up to replace Joe Oliver as Jorge Posada‘s backup.