He was the son of James Vanderpool Wemple (1820–1900) and Margaret Ann (Kaley) Wemple (1835–1918). He attended the district schools, Union Classical Institute, and Union College. Then he taught school, and was Principal of the Scotia village school. Then he studied law, graduated from Albany Law School in 1886, was admitted to the bar the same year, and practiced. In 1894, he married M. Adelaide Quaife, and they had five children, among them Assemblyman William W. Wemple, Jr. (1898–1972).
