Murray was born in Newcastle. After attending Eton and Cambridge, he distinguished himself at University College Hospital. Then, after visits to Berlin and Paris, he returned to Newcastle and began work as pathologist to the Hospital for Sick Children, and lecturer in bacteriology in the Durham University College of Medicine. Early in his career he made the discovery which brought him fame - that injections of an extract of thyroid gland could cure myxodemia. Murray published his results in 1891 and, with typical care, he followed up the case of a woman thus cured until 1920. Murray's discovery opened up a whole field of inquiry, particularly into the function of the endocrine glands and their influence on health and personality.
With his reputation established, Murray took on the posts of professor of comparative pathology at Durham in 1893 and physician to the Royal Victoria Infirmary in 1898. He held these posts until 1908, when he moved to Manchester to become Professor of Medicine. He remained there for the rest of his life, a much loved and admired figure.