Boynton was the eldest son of the Reverend Henry Boynton, Rector of Barmston. He inherited the baronetcy on 22 December1731, on the death of his cousin Sir Griffith Boynton, who had no children. He served in Parliament as member for Hedon from 1734 until his death five-and-a-half years later.
On 8 April1703, he married Frances Heblethwayte, daughter of James Heblethwayte, and they had three children: