Born in London, he was younger son of Robert Tyrwhitt (1698–1742), residentiary canon of St Paul's Cathedral, by his wife Elizabeth, eldest daughter of Edmund Gibson, bishop of London.
He entered as a pensioner at Jesus College, Cambridge on 9 March 1753, and graduated B.A.
He was one of the founders of the London Unitarian Society (1791), precursor of the British and Foreign Unitarian Association which led in turn to today's General Assembly of Unitarian and Free Christian Churches, but on the introduction into its preamble of the term ‘idolatrous,’ as applied to the worship of Jesus Christ, he withdrew his name and cancelled his donation.
He published two sermons preached before the university, and a reprint (1787) of his two papers in Commentaries and Essays.
He left money to the University of Cambridge, used to found the Tyrwhitt Hebrew scholarships.