He was born at Waulkmill, Cruden, Aberdeenshire, and baptised there on 15 March 1714, the son of Robert Kilgour and Isobel Barron.

[1] He was educated at King's College, Aberdeen from 1729 to 1733; graduating with a Master of Arts degree on 29 March 1733.

[1] One of their daughters, Christian, married Patrick Torry (later Bishop of St Andrews, Dunkeld and Dunblane) in 1787.

[1] Fourteen years later, Kilgour also became the Primus of the Scottish Episcopal Church on 25 September 1782.

[1][2] He resigned as Bishop of Aberdeen in 1786, and as Primus in 1788, both post were succeeded by his Coadjutor, John Skinner.