Dempsey replaces Jerry Colangelo, who held the position for two terms but will now focus on his role as managing director of the U.S. men's national team.
Dempsey was elected Monday during a meeting of USA Basketball's board of directors. His term is 2017-2020.
He retired last year after 41 years in the military, the last four as the senior officer in the Armed Forces and the military adviser to the secretary of defense and the president. He was appointed special adviser to NBA Commissioner Adam Silver in January.