Dorrance was born in Bombay, India on April 9, 1951, the son of an American oil executive. He spent his youth moving with his family throughout Europe and Africa. Of all the places he lived, three had particular influences on his later life. In Addis Ababa, Ethiopia he met his future wife, M'Liss Gary, the daughter of the U.S. Air Force attache to Ethiopia. He attributes his love of soccer to his years living in Kenya and finally, he gained his education from the boarding school, Villa St. Jean International School, in Fribourg, Switzerland from which he graduated in 1969.