Greene studied at the Academy school, the Art Students League, New York, and with Philip Guston at the State University of Iowa, Iowa City. An abstractionist in his mature work, he is noted for his creation of a personal vocabulary of symbols, expressive of essential themes of Christianity, and explorations of the dark side of human psychology.
He received a Prix de Rome, providing study and residence at the American Academy in Rome, 1952-54, and again passed two years in Rome, 1972-74. Other awards and grants were received from the Corcoran Gallery of Art, 1965; the Council of Arts and Letters, 1966; the American Institute of Arts and Letters, 1967. In Academy annual exhibitions he has received the Carnegie Prize, 1971; the Puzinas Memorial award, 1981; the Saltus Medal, 1983; and an Obrig prize, 1985 and 1989. He has taught at Princeton (New Jersey) University the Art Students League; the Tyler School of Art, Philadelphia; and the Skowhegan (Maine) School of Art.
Greene's paintings are held in major public and corporate collections throughout America and abroad. Major retrospectives of his work have been held at the Corcoran Gallery, Washington, D. C., in 1963, and at the Akron (Ohio) Art Institute, in 1978.
In 1988, Greene was elected to a three-year term on the Council. He resides in Valley Cottage, New York, and is represented by the Marilyn Pearl Gallery, New York.