Thompson attended Edinburgh Academy and studied medicine at the University of Edinburgh, publishing papers in scientific journals on hydroid taxonomy, or the classification of invertebrate animals, at age nineteen. Eventually leaving Edinburgh, Thompson attended Trinity College, Cambridge, where he tutored Greek to pay for his tuition. He also translated Herman Müller's German work "The Fertilisation of Flowers," which was published with a preface by the naturalist Charles Darwin.

Thompson began his career as a professor of biology at the University College in Dundee in 1884. He worked at the university throughout his life, establishing a teaching museum of zoology and writing papers on various zoological subjects. In 1896, Thompson traveled to Alaska to investigate a dispute between Great Britain and the United States over fur-seal expeditions. The following year, he was recognized for his efforts, earning the title of Companion of the Order of Bath in...