Born in Stonecroft, near Hexham, Northumberland on 2 February 1738,[1] the son of Jasper Gibson and Margaret Gibson (née Leadbitter).[2] He was sent for his education to Douai and served as president of the college from 1781 to 1790.[1]
When the English College at Douai was forced to close in 1795 following the French Revolution, some of the students were settled temporarily at Crook Hall northwest of Durham. In 1804 Bishop Gibson began to build at Ushaw Moor, four miles west of Durham. These buildings, designed by James Taylor, were opened as St Cuthbert's College in 1808.
Bishop Gibson resided principally at York, although sometimes with the resident priest at Durham, Thomas Smith, who, in 1810, he requested as his coadjutor. In 1819, becoming increasing more frail in mind and body, his powers to transferred to Bishop Smith.
He died in office on 2 June 1821, aged 83, at Ushaw and was buried in the college cemetery at Ushaw College[6] which he himself had founded in 1804.