Alexander Williams was born in County Monaghan and was educated at Drogheda Grammar School. He became a painter in oils and water-colours, having studied drawing at the Art School of the Royal Hibernian Academy. In 1883 he was elected an Associate of the Royal Hibernian Academy and a member eight years later. Many of his paintings were Irish landscapes, and he exhibited in Australia, Canada and England. He was also a soloist in many Dublin choirs.