Greene was born on 19 January 1794, the only son of Thomas Greene of Slyne and Whittington and Martha Dawson, daughter and co-heiress of Edmund Dawson of Warton. His father, a barrister, chambers in Gray's and a house in Bedford Square.[7]
Greene was first elected Tory MP for Lancaster at a by-election in 1824 and held the seat until 1852—becoming a Conservative in 1834, and a Peelite around 1847. He later regained the seat at a by-election in 1853—caused by the unseating of Robert Baynes Armstrong due to corruption and bribery—but stood down at the next election in 1857.[8][9]
On 30 August 1820, Greene married Henrietta Russell (d. 1882), a daughter of Sir Henry Russell, 1st Baronet, of Swallowfield. Together, they were the parents of three sons and two daughters, including:[7]
Dawson Cornelius Greene (1822–1887), an Army Officer who married his cousin, Mary Russell, daughter of Sir Henry Russell, 2nd Baronet.[13]
Thomas Huntley Greene (1823–1887), a Reverend who married Helen Stuart, youngest daughter of Gen. Hon. Sir Patrick Stuart (a son of Alexander Stuart, 10th Lord Blantyre), in 1857.[13]
Henry Aylmer Greene (1827–1877), who died unmarried.[13]
After a long illness, Greene died at Whittington on 8 August 1872.[7] On Greene's death, Whittington Hall passed to his eldest son, Dawson, who retired to live in London and was succeeded by his son, Henry Dawson Dawson-Greene.[11]