George Greene was born on April 20, 1914, in Laurens, South Carolina. He was commissioned through the Army ROTC program at Clemson University on May 31, 1935, and went on active duty beginning February 20, 1937, when he entered the Aviation Cadet Program. Greene was awarded his pilot wings at Kelly Field, Texas, on February 17, 1938, and then served with the 35th Pursuit Squadron of the 35th Pursuit Group at Langley Field, Virginia, and Mitchel Field, New York, from February 1938 to December 1941. He became the commander of the 35th Pursuit Squadron in December 1941, and moved with the squadron to New Guinea that same month, serving there until March 1943. During this time, Col Greene was credited with the destruction of 3 enemy aircraft in aerial combat plus 4 on the ground and 1 in the water. He briefly commanded the 423rd Reconnaissance Group at De Ridder, Louisiana, from April to August 1943, and then served on the staff of 3rd Fighter Command, 3rd Air Force, and at Tactical Air Command at Drew Field, Florida, and then at Langley Field, Virginia, from September 1943 to September 1947. Col Greene was Chief of Staff of the 6th Fighter Wing in Panama from October 1947 to July 1948, and then served on the staff of Caribbean Air Command from August 1948 to August 1950. His next assignment was as Chief of Combat Operations and Training at Eastern Air Defense Force in Stewart, New York, from August 1950 to August 1951, and then as Commander of the 113th Fighter Wing (later redesignated the 4710th Air Defense Wing) at New Castle County Airport, Delaware, from August 1951 to August 1952. He attended Air War College at Maxwell AFB, Alabama, from August 1952 to July 1953, and then served as Commander of the 4708th Air Defense Wing at Selfridge AFB, Michigan, from July 1953 to July 1956. Gen Greene then served on the staff of Air Defense Command at Ent AFB, Colorado, from July 1956 to August 1960, followed by service as Deputy Commander of 17th Air Force at Ramstein AB, West Germany, from August 1960 to August 1961. He was Deputy Chief of Staff for Operations with U.S. Air Forces in Europe at Lindsey AFS, West Germany, from August 1961 to July 1963, and then Director of Military Personnel at Headquarters U.S. Air Force in the Pentagon from July 1963 to July 1965. Gen Greene was Assistant Deputy Chief of Staff for Personnel at Randolph AFB, Texas, from July 1965 to June 1967, and then served as Commander of the Lackland Military Training Center at Lackland AFB, Texas, from July 1967 until his retirement from the Air Force on August 1, 1970. George Greene died on October 15, 1998, and was buried at the Fort Sam Houston National Cemetery in San Antonio, Texas.

His Distinguished Service Cross Citation reads:

The President of the United States takes pleasure in presenting the Distinguished Service Cross to George B. Greene, First Lieutenant (Air Corps), U.S. Army Air Forces, for extraordinary heroism in connection with military operations against an armed enemy while serving as Pilot of a P-38 Fighter Airplane in the 35th Fighter Squadron, 8th Fighter Group, FIFTH Air Force, in aerial combat against enemy forces in the Southwest Pacific Area, during World War II. First Lieutenant Greene's unquestionable valor in aerial combat is in keeping with the highest traditions of the military service and reflects great credit upon himself, the 5th Air Force, and the United States Army Air Forces.