He began a medical degree at Edinburgh, but suffered from ill health, prompting him to break his studies and visit Australia.
He visited the South Seas and spend some time living in the New Hebrides, where he collected plants for Ferdinand von Mueller.
Plant taxa published by him include Acacia densiflora, Acacia longispinea, Angianthus acrohyalinus (Hook-leaf Angianthus), Calandrinia creethae, Calandrinia schistorhiza, Drosera bulbigena (Midget Sundew), Drosera occidentalis (Western Sundew), and Indigofera boviperda.
In 1912 he was appointed assistant botanist to Alfred Ewart at the National Herbarium of Victoria (MEL).
[2] Alexander Morrison National Park, north of Perth in Western Australia, is named in his honour.