William was born on April 29, 1850 at Boston, Massachussets, United States. He was the eldest son of Isaac and Elizabeth B. (Woodberry) Story. He also was descended from Elisha Story, who came from England to Boston about 1700. Joseph Story, associate justice of the United States Supreme Court for many years, was a brother of his grandfather; and his great-grandfather, Dr. Elisha Story of Bunker Hill, was one of the "Indians" of the Boston Tea Party.