He toured with and arranged for big bands led by Orville Knapp, Freddy Martin, Horace Heidt, Wayne King, Xavier Cugat, and Harry James.
Greene started his career in scoring cartoons at the Walter Lantz Studio, first credited in the 1963 Greedy Gabby Gator Woody Woodpecker short.
Around 1966, he started providing musical scores for some Pink Panther animated shorts (as well as those of The Inspector), replacing William Lava.
Unlike the music scores composed by Bill Lava, which were custom made for a specific entry, his compositions were generic and could be reused more freely.
Greene also composed musical scores for the 1966 Tarzan TV series with some episodes linked together for feature film release and The New Three Stooges (1965).