Born in Potowomut, Warfield Township, Rhode Island. Elected to the Rhode Island Legislature. Married Catherine Littleford July 20, 1774. They had five children. Trained as a blacksmith.

Served as a general during the revolutionary war. He served during the seige of Boston and commanded the army of occupation in 1776. He fought with Washington at Trenton, Brandywine, Germantown and Monmouth. In March 1778 he became quartermaster general. He replaced Horatio Gates after the defeat in South Carolina. He was in command at the battle of Eutaw Springs September 8, 1781. After the defeat of Cornwallis at Yorktown ended the war, the siege at Charleston continued for another year. He died of sunstroke at his plantation near Savannah, Georgia.

Congress honored Greene with a medal (Betts 597) by resolution October 29, 1781, for the victory at Eutaw Springs. The original was struck in Paris in 1787. Restrikes (Julian MI-10) were struck in Philadelphia after 1886. Modern bronze restrikes (USM 408) were also produced. A 38 mm pewter Greene medal was included with "America's First Medals" produced about 1976.

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