Born in Warwick, Rhode Island, Greene was a son of William Greene Jr. and Catharine Ray. His father was a governor of Rhode Island during the American Revolutionary War, and his mother was a correspondent of Benjamin Franklin. Greene pursued classical studies and graduated from Yale College in 1784, then studied law, was admitted to the bar, and commenced practice in Providence. He was attorney general of Rhode Island from 1794 to 1797, and in the latter year was elected as a Federalist to the United States Senate to fill the vacancy caused by the resignation of William Bradford. Greene was reelected in 1799 and in total served from November 13, 1797, to March 5, 1801, when he resigned, having been nominated for a judicial position. He was designated a district judge of Rhode Island by President John Adams, but, through a technicality, was not appointed.
Family
Greene married in Charleston, South Carolina, on July 23, 1794, Mary Magdalene Flagg (1775–1817), the daughter of George Flagg and Mary Magdalene Henderson of Charleston. The couple had five children, the oldest of whom was George Turner Greene (1795–1821) followed by William Greene III who became a Lieutenant Governor of Rhode Island in the late 1860s. Their third child, Catharine Ray Greene (1799–1875) married in 1815 Dr. James Varnum Turner; Mary Elizabeth (born 1804) died as a youngster; and Isabella Mary (1805–1863) married in 1833 Joseph S. Jenckes.[1]