In 1867 he entered the British Museum as an assistant in the department of Greek and Roman antiquities under Sir Charles Newton, whom he succeeded in 1886. His younger brother, George Robert Milne Murray (1858-1911), was made keeper of the botanical department in 1895, the only instance of two brothers becoming heads of departments at the museum. In 1873 Dr Murray published a Manual of Mythology, and in the following year contributed to the Contemporary Review two articles--one on the Homeric question--which led to a friendship with Mr Gladstone, the other on Greek painters. In 1880-1883 he brought out his History of Greek Sculpture, which at once became a standard work. In 1886 he was selected by the Society of Antiquaries of Scotland to deliver the next years Rhind lectures on archaeology, out of which grew his Handbook of Greek Archaeology (1892).
In 1894-1896 Murray directed some excavations in Cyprus including those at Enkomi. These were undertaken by means of a bequest of £2000 from Miss Emma Tournour Turner. The objects obtained are described and illustrated in Excavations in Cyprus, published by the trustees of the museum in 1900. Murray's other official publications include three folio volumes on Terra-cotta Sarcophagi, White Athenian Vases and Designs from Greek Vases. In 1898 he wrote for the Portfolio a monograph on Greek bronzes, founded on lectures delivered at the Royal Academy in that year, and he contributed many articles on archaeology to standard publications.