He was the son of Alexander Falconer, an Elgin merchant, and Jean King.
[1] His grandfathers were the Reverend William Falconer (the son of Right Reverend Colin Falconer, Bishop of Argyll (1679–80) and Bishop of Moray (1680–86)), and William King of Newmill, Provost of Elgin (1690–1700).
[1][2] He was appointed coadjutor bishop of Caithness and Orkney and consecrated at Alloa on 10 September 1741 by Thomas Rattray, Primus of the Scottish Episcopal Church, with bishops Robert Keith and Robert White serving as co-consecrators.
[1] He was unanimously elected Primus of the Scottish Episcopal Church at Forfar on 24 June 1762, and also became the Bishop of Edinburgh on 25 October 1776.
[1][2] He resigned the see of Moray before May 1778 and the office of Primus in September 1782, but retained the see of Edinburgh.