When Richard Greene was born on 4 December 1769, in Warwick, Kent, Rhode Island, United States, his father, Griffin Greene, was 20 and his mother, Sarah Greene, was 17. He married Bathesheba Rouse on 17 July 1794, in Washington, Ohio, United States. They were the parents of at least 3 sons and 1 daughter. He died in December 1805, in Marietta, Washington, Ohio, United States, at the age of 36, and was buried in Mound Cemetery, Marietta, Washington, Ohio, United States.