Greene came from a prosperous yeoman family resident at Water Orton in north-west Warwickshire. In 1596 his father bought Wyken manor, which Greene inherited two decades later, along with the local parish tithes and some 20 acres in the same district. He was wealthy enough by 1621 to contemplate investing £2,500 in a Leicestershire estate, and towards the end of the decade his eldest son acquired a coat of arms. One of the more prominent gentlemen living in the county of Coventry, he was selected by the Privy Council in 1624 to investigate complaints by the city’s corporation about a local mining venture.
In Coventry’s 1628 parliamentary election, Greene stood successfully against one of the city’s leading aldermen, Isaac Walden*, winning the poll emphatically by 367 votes to 29. His motive for standing is unclear, but he was probably invited to do so by a disaffected element within the corporation which was opposed to Walden. A contemporary newsletter claimed that Greene and his running-mate, William Purefoy*, were both Forced Loan refusers, implying that this factor influenced the outcome. However, while Purefoy certainly opposed the Loan, and a number of Greene’s neighbours in Wyken did likewise, there is no evidence that he himself refused.
Greene confirmed his local status by serving as a subsidy commissioner at Coventry in 1628-9, and in a similar capacity there in 1641-2. He drew up his brief will on 6 July 1652, requesting burial in Wyken church alongside his late wife. He had already made provision for his younger children, and arranged for his debts to be cleared. His property by this stage included a small estate at Sutton Coldfield, a few miles from his ancestral home of Water Orton. He was dead by September 1653, when his will was proved.