William Greene III (January 1, 1797 – March 24, 1883) was a lieutenant governor of the state of Rhode Island, serving for two years shortly after the American Civil War.

From a prominent Rhode Island family, Greene was the son of United States Senator and Rhode Island Attorney General Ray Greene and his wife Mary M. Flagg.

"[1] Greene graduated from Brown University and studied law at Litchfield in Connecticut.

Following this he went to Ohio about 1820, and spent more than four decades there, promoting the Cincinnati public schools and roads.

[2] Greene delivered a Phi Beta Kappa Address at Brown in 1851, which supported the Fugitive Slave Act of 1850 and criticized those who violated the law (abolitionists).