Born in Paisley, Renfrewshire, Armour studied art at Glasgow School of Art 1918–23 under Maurice Greiffenhagen, where he met his wife, the painter Mary Armour, whom he married in 1927. He was a painter in oil and watercolour as well as a draughtsman in pastel and wood engraver. Armour joined the staff of Glasgow school of Art in 1947 and became head of drawing and painting in 1955, retiring in 1957. He exhibited at the Royal Scottish Academy, the Royal Society of Painters in Water colour as well as the Glasgow Institute.
His work is held widely in public collections in Scotland, and elsewhere. He lived at Kilbarchan, Renfrewshire.