Armstrong was born in 1780 at Ballynahinch, county Down. He was the son of John Armstrong, who married a daughter of Review John Strong, for thirty-six years (1744–1780) presbyterian minister of Ballynahinch.
He was a descendant of John Livingstone, of Killinchy, one of the founders of Irish presbyterianism.
He graduated at Trinity College, Dublin, and studied philosophy in Edinburgh University under Dugald Stewart.
He was first trained at the Rademon Academy, under Moses Neilson, Doctor of Divinity, after which he became classical assistant to William Bruce at Belfast Academy, and conducted a special class of sacred history. He was licensed 11 May 1806 by Antrim Presbytery (non-subscribing). In the previous year he had received the degree of Doctor of Divinity from the university of Geneva.
A petition from his widow is printed in Parliamentary Debates on the Dissenters" Chapels Bill, 1844.
He was a member of the Royal Irish Academy.
