William Johnson received his schooling in the city of Durham and then qualified in Edinburgh in 1882 as a licentiate of the Royal College of Surgeons (LRCS) of Edinburgh, a licentiate of the Royal College of Physicians (LRCP) of Edinburgh, and a licentiate in midwifery of the Royal College of Physicians (LMRCP) of Edinburgh. During his studies he was awarded the gold medal in chemistry in 1880. He became a member of the British Medical Association and in 1886 published a paper on "Four cases of cornea grafting" in the British Medical Journal.
In 1889 he came to the Orange Free State, where he was registered to practise in May 1889, and settled in Bloemfontein. Some years later he advertised in a local periodical that he was a surgeon, physician, obstetrician, and specialist in eye and ear sicknesses. He became a member of the (second) South African Medical Association and in 1894 published a note on "A case of exophthalmic goitre" in its Journal. At some stage he acted as surgeon for the Kaffer River section of the railway, just south of Bloemfontein. After the Anglo-Boer War he served as a member of the medical council of the Orange River Colony (now the Free State). He was still listed as practising in Bloemfontein in 1916.
Johnson's hobbies were chemistry and physical science, which resulted in some publications pertaining to geology. At the annual congress of the South African Association for the Advancement of Science in 1909 he read a paper on "The origin and formation of the diamond", which was published in the association's Report for that year (pp. 167-180). He became a member of the association around this time and in 1912/3 represented Bloemfontein on its council. In 1914 he delivered a paper with an identical title, but presumably an updated content, at the annual congress (Report, 1914, pp. 275-285). Meanwhile he had contributed another paper, "Note on xenoliths in gabbro near Belfast, Transvaal", to the Transactions of the Geological Society of South Africa in 1911.