William Wolcott Green was born around 1840 in South Windsor, Connecticut, to William and Jane Green. His father was a farmer who owned $3,500 of real estate and $560 of personal property by 1860. Green grew up and attended school in South Windsor, and by 1860, he was working as a farm laborer.
He enlisted in the Union army on August 25, 1862, and he mustered in as a private in Company G of the 25th Connecticut Infantry on November 11. The regiment took part in the siege of Port Hudson, and he mustered out on August 26, 1863.
He returned to South Windsor after leaving the army, and he married Harriet Elmer around 1866. They had at least two children: Alice, born around 1866; and Carrie, born around 1874. He worked as a farmer in South Windsor, and he employed at least one farm laborer. He applied for a federal pension in August 1890 and eventually received one. His wife died on February 8, 1904, and he married Della Gaines on June 7, 1905. He died of peritonitis in Granby, Connecticut, on February 25, 1913.