William Greenwell was born 23 March 1820 at the estate known as Greenwell Ford near Lanchester, County Durham, England. He was the eldest son of William Thomas Greenwell (1777–1856) and Dorothy Smales. He had three brothers Francis, Alan (vicar of Haydock), and Henry, and a sister Dorothy (1821–1882) who published poetry under the name Dora Greenwell.
