Born in Glasgow, Shannan began his career as an apprentice stonemason to his father. This led to him travelling to the Cameroons, West Africa, to help supervise the construction of sanatoria and then on to the USA, where he oversaw the construction of state buildings in Texas. Back in the UK, Shannan attended the Royal College of Art in London, before studying painting, sculpture and anatomy at the National Art Training School in Paris for around eight years. In 1892 he returned to Glasgow and began his career as a sculptor. He produced many important sculptures in marble and bronze alongside the stone statue of the poet, John Barbour, who features on the south-east tower of the Scottish National Portrait Gallery.