Arthur Fuller was a son of Sir Thomas E. Fuller, Cape parliamentarian and journalist, and older brother of Dr E. Barnard Fuller*. Arthur came to the Cape with his parents in 1864. He received his schooling in Cape Town, partly at the South African College, where he was registered from 1870 to 1873. Proceeding to Scotland he qualified as Bachelor of Medicine (MB) and Master of Surgery (CM) at the University of Edinburgh in 1883 and as a member of the Royal College of Surgeons of England in 1884. After serving as house surgeon at the Royal Infirmaries in Edinburgh and Glasgow and then as resident medical officer at the Hackney Union Infirmary for a short time, he returned to South Africa in 1885 and took over the practice of his brother-in-law, Dr A.H. Watkins, in Boshof, Free State. On 27 January 1887 he was licensed to practice in the Cape Colony and soon joined Dr Watkins in Kimberley. Based on his experience in the Free State he wrote South Africa as a health resort, with especial reference to the effects of the climate on consumptive invalids, and full particulars of the various localities most suitable for their treatment.... The booklet was originally published in London in 1886 and was so well received that a sixth edition appeared in 1898.
In Kimberley Fuller soon established himself as a prominent member of the medical fraternity. In 1887 his appointment as honorary pathologist to Kimberley Hospital was one of the first two specialist appointments in South Africa, other than in the fields of medicine and surgery. That same year he was elected as the first secretary of the newly founded Griqualand West Medical Association. He also became consulting surgeon to the Kimberley Hospital, surgeon to the local Volunteer Corps, railway medical officer, town councillor, and a member of the local school board. In February 1889 he was elected honorary treasurer of the newly established Griqualand West Branch of the British Medical Association (BMA), successor to the Griqualand West Medical Association. As joint secretary of the first Medical Congress in South Africa, held in Kimberley in May 1893, he was partly responsible for the organisation of this important event. At the congress he introduced a two-fold motion. His first proposal was that a South African Medical Association (the second with this name) be formed. However, as local branches of the British Medical Association had recently been established this proposal was not adopted at the time. It was only acted upon four years later, and he became a member of the new Association. His second proposal was that a South African Medical Journal (also the second with this name) be established, and this was adopted. Fuller contributed an article to the first issue of this new journal under the title "A medical journal for South Africa", in which he justified its formation. He continued his participation in organised medicine with his election as president of the Kimberley Branch of the BMA in July 1894, and as treasurer of the branch in December 1895.
Fuller, like his younger brother, was a sportsman of note. In 1892 he won the Western Province tennis championship held during the Kimberley Exhibition, and as a cyclist he toured many parts of the subcontinent. He remained in Kimberley and died there as a post-epidemic victim of influenza. He was married to Katrina A.R. Fuller, born Niemeyer.