Private First Class Greene was a member of Company I, 3rd Battalion, 187th Airborne Infantry Regimental Combat Team. He was Killed in Action while fighting the enemy in North Korea on 21 October 1950. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Greene was awarded the Purple Heart, the Combat Infantryman's Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.