"The conversion to Islam is not abandoning Christianity or Judaism, which I was born with. It means I have accepted Muhammad and other prophets," he said from the Iranian city of Isfahan, where he reportedly underwent his conversion ceremony.
Iran's Fars news reports that Stone became a Shiite and chose the Muslim first name Ali.
Stone's director father is Jewish, and his mother is Christian.
Stone, 27, has directed several documentaries and had bit parts in his father's films, AFP reports.