Career
Born in Stonecroft, near Hexham, Northumberland on 23 March 1734, the son of Jasper Gibson and Margaret Gibson (née Leadbitter). He was ordained to the priesthood in 1758. Matthew was appointed the Vicar Apostolic of the Northern District and Titular Bishop of Comana Armeniae on 17 June 1780.
He was consecrated to the Episcopate by Bishop James Robert Talbot on 3 September 1780.
He died in office at Stella Hall, County Durham on 17 May 1790, aged 56.