[8] John attended Horace Mann School and the New York Military Academy, and was accepted by Harvard at the age of 15, entering the university in 1924.

Disliking the job, and encouraged by his wife, the former Carol Faulk, John left Wall Street to pursue a musical career.

It was while writing material for Gertrude Lawrence in 1930 that he composed "Body and Soul", the first recording of which was made by Jack Hylton & His Orchestra eleven days before the song was copyrighted.

Between 1930 and 1933, Green was the arranger and conductor for Paramount Pictures and worked with such singers as Ethel Merman, Gertrude Lawrence and James Melton.

During his two and a half years at Paramount Astoria, he was able to learn more about film scoring from veterans Adolph Deutsch and Frank Tours.

The orchestra, based for a time at the St. Regis, featured Green's piano and arrangements, whose harmony and mood were among the most sophisticated of the day.

His regular cast included his band singers Marjory Logan and Jimmy Farrell, essayist Christopher Morley, and stage/screen favorites the Four Eton Boys.

He continued conducting on radio and in theatres into the 1940s, also leading a dance band for the short-lived Royale Records label in 1939–1940, until he decided to move permanently to Hollywood and work in the film business.

Green particularly made an impression at Metro-Goldwyn-Mayer, where in the 1940s, along with orchestrator Conrad Salinger, he was one of the musicians most responsible for changing the overall sound of the MGM Symphony Orchestra, partially through the re-seating of some of the players.

Nominated for an Oscar thirteen times, he won the award for the musical scores of Easter Parade, An American in Paris, West Side Story, and Oliver!, as well as for producing the short "The Merry Wives of Windsor Overture", which won in the Short Subjects (One-Reel) category in 1954.

The short subject featured Green conducting the MGM Orchestra on-screen in the music from the opera of the same name by Otto Nicolai.

He also continued to compose the occasional score to films such as Twilight of Honor (1963), Johnny Tiger (1966) and Alvarez Kelly (1966), and contributed the arrangements and musical direction for the critically acclaimed They Shoot Horses, Don't They?

He recruited a team which included set designer Grant Major and Oscar-nominated director of photography Wally Pfisher to complete the job.

As mentioned earlier, Green conducted the orchestra for such famous MGM musicals as An American in Paris, as well as for United Artists' 1961 film version of West Side Story.