Born in Edinburgh in 1891 to Robert and Marion Anthony, John Anthony attended George Heriot's School and Edinburgh University, reading Arts and Science. His studies were interrupted by the First World War, with him spending eight years in service in France, Italy (where he won a Military Cross in 1918[?]), Egypt and Palestine, resuming University life in 1923.
After graduating in 1924 he worked on a rubber plantation in Malaya for five years, before becoming an assistant lecturer in Botany at the University College in Dundee on his return in 1932. In 1934 he became a lecturer in Forest Botany (amongst other things) at the University of Edinburgh, and so began his career with the Royal Botanic Garden Edinburgh. He was a member of the teaching staff for 24 years, retiring in 1958. In his retirement he worked on producing a guide for indentifying trees, shrubs and undershrubs by their microscopic properties, and a Flora of Sutherland - the latter being published posthumously by the Botanical Society of Edinburgh [Scotland].