Son of William Smith, who married in 1657 Elizabeth, daughter of Giles Wetherall of Stockton, he was born at Lowther, Westmorland on 10 November 1659, one of 11 brothers, who included Joseph Smith and others well known in their time.
In 1696 Smith was created D.D. at Cambridge, and three years later was made treasurer of Durham, to which the bishop added in July 1704 the rectory of Bishop-Wearmouth.