Wharton entered the navy in August 1857. Made captain in 1880. In August 1884 he was appointed hydrographer of the navy in succession to Sir Frederick Evans, and held this post until August 1904, becoming the longest serving hydrographer after Sir Francis Beaufort. Died in Cape Town in 1905 of enteric fever while visiting as acting president for the geographical department of the British Association for the Advancement of Science.