George Redmayne Murray was educated at Trinity College, Cambridge University where he studied natural sciences, and at University College Hospital London. He qualified in 1889. He worked at University College Hospital with Victor Horsley where they carried out original work on use of thyroid gland grafts to treat myxoedema. Murray also discovered that cretinism was linked with defective thyroid. Murray was therefore considered one of the founders of endocrinology.
In 1891 Murray was appointed pathologist at the Hospital for Sick Children, Newcastle-upon-Tyne, and was Heath Professor of comparative pathology at Durham University from 1893-1908. In 1908 he was appointed professor of systematic medicine at the University of Manchester and retired in 1925. He was a member of the Medical Research Council, president of the Association of Physicians of Great Britain and Ireland and a member of the departmental committee of the Home Office which investigated dust in the card rooms of cotton factories.