Alexander studied at the Royal Institution, Edinburgh from 1887-8, and in Paris with the sculptor Emmanuel Frémier.

In 1887-8 the artist travelled to Tangier with his father and fellow artists Pollock Nisbet and Joseph Crawhall. He returned to Egypt in 1892, after his artistic studies, and lived on a houseboat on the Nile for 4 years, painting in the desert. This drawing appears to be of North Africa, the evocative rooftops an engaging subject on the characteristic oatmeal paper he often used.

In 1902 Alexander was elected an associate of the Royal Scottish Academy becoming a full member in 1913. He exhibited widely including at the Royal Scottish Academy, Royal Academy, Fine Art Society, Royal Watercolour Society and the Leicester Galleries.

Alexander’s work is held in the Tate Gallery, Aberdeen Art Gallery, Dundee Art Gallery and by Fife Council.