Welsh was born at Braefoot Farm near
Moffat on 11 December 1793, the youngest of 12 children of David Welsh, a sheep farmer at Earlhaugh and Tweedshaws, He was educated at Moffat Parish School, and tutored at home by Rev McWhir, later minister of Urr in Galloway, then David was sent to the High School in Edinburgh. He studied divinity at the
University of Edinburgh and was licensed to preach in 1816 by the Presbytery of
Lochmaben. In 1821 he was ordained as minister of
Crossmichael. From there he was translated to St David's Church in
Glasgow.
Glasgow University granted him a
Doctor of Divinity (DD) in 1831. In the 1820s, Welsh was notable for his attempt to forge an alliance between the evangelicals and the
Edinburgh Phrenological Society - then at the height of its influence. However, Welsh was out-manoeuvered by
George Combe - the "high priest" of the phrenologists - who prohibited all discussion of religious matters at phrenological meetings. Welsh and his fellow evangelicals then left the society. In 1831 he was appointed professor of
ecclesiastical history in the
University of Edinburgh. In 1834 he was elected a fellow of the
Royal Society of Edinburgh, his proposer being Sir William Hamilton. He is seen on the Disruption Painting by
Hill to
Thomas Chalmers's right holding the protest he read to the Church of Scotland assembly. He was secretary of the Scottish Bible Board and also editor of the
North British Review. He retired to Drumfork House near
Helensburgh in his final years. He died of a heart attack on 24 April 1845 at Camus Eskan in
Dumbartonshire, and is buried against the western outer wall of the southern section of
St Cuthbert's churchyard in
Edinburgh. ==Family==