Mellanby was born at West Hartlepool, the son of the manager of the Furness-Withy shipyard. Elder brothers were John Mellanby, (1878-1939), the physiologist, and Alexander Lawson Mellanby (1871-1951), professor of civil and mechanical engineering at the Royal Technical College, Glasgow. At Barnard Castle School, Mellanby was head boy and captain of cricket and football. After Cambridge, he worked in London and after 1920, held the chair in pharmacology at Sheffield, as well as becoming secretary of the Medical Research Council.
Mellanby is best known for his research into rickets, which he established was caused by a lack of vitamin D, but his work extended over a very wide range and he was recognised as an outstanding expert in the biochemical and physiological field. Tall and handsome, and possessed of an attractive boyishness, Mellanby could seem brusque, as he bent all his attention on the question, rather than the questioner. As a friend remarked of him: 'What a listener thought of him temporarily did not matter, so long as medical science was advanced or a new scientist born.'