Alexander Webster was born in Scotland the second son of James Webster, the Minister of the Tolbooth Parish in Edinburgh. Alexander was appointed to his father's parish after serving at Culross from 1733-37. Culross is in Fifeshire on the north shore of the Firth of Forth about 15 miles from Edinburgh.

Alexander Webster was the Moderator of the General Assembly in 1753 and the Dean of the Chapel Royal in 1771.

In addition to his clerical work he published verses in "The Scots Magazine" and set up various financial schemes to provide for the retirement and care of the clergy. He was so highly regarded for his numerical skills that he was entrusted with what was known as "Webster's Census" which in 1755 showed the Scottish population as 1,265,000.

Alexander Webster had ten children over a period of 16 years. His notable son James Webster was a distinguished Brigadier under the British General Cornwallis during the American War of Independance, and father of Joseph Webster I.

A portrait of Dr Alexander Webster (1707-1784) hangs in the Widow's Hall of the Fund Office (for the retirement of the clergy) of the Church of Scotland in Edinburgh.