He attended the Boston Latin School and graduated from Harvard in 1879. After five years spent in study in Europe, including fifteen months in Greece and three semesters at the University of Berlin, he returned to Boston in 1885 and became curator of classical antiquities at the Museum of Fine Arts.
He was elected its director in 1902, holding this position until 1905, when he went to New York as assistant director and curator of classical art at the Metropolitan Museum of Art. In 1910 he was elected director, remaining in office during his lifetime. He was the third to hold the chief administrative position, and the first of American parentage. Robinson's administration was notable. His first care was the assembling of a scientific staff and the organizing of departments with a competent curator at the head of each. His own chosen field was classical archaeology, and he set the same high standard for the classical department of the Metropolitan Museum that had made the collection in the Boston Museum outstanding, but he was equally interested in the development of other departments, which all came under the influence of his sound judgment and unerring taste. Several new wings were built to house the rapidly growing collections, many of which, coming as gifts or bequests, presented special problems in their exhibition and care. At the same time the increased use of the Museum by the public made necessary constant cooperation in the way of publications, lectures, and temporary exhibitions. A new stage of Museum development was reached with the establishment, in 1925, of a branch museum, The Cloisters, and the series of symphony concerts given each winter after 1919. In spite of all these activities, which made so great a demand on the time of the Director, he found it possible to serve on the boards of several other institutions. He was a member of the Council of the Archaeological Institute of America and president of its New York society; a member of the managing committee of the American School of Classical Studies in Athens; a trustee of the American Academy in Rome; a member of the Executive Committee of the American Society for the Excavation of Sardis; a director of the American Federation of Arts; a trustee of the Museum of the City of New York, and a member of the Commission for the Excavation of the Agora of Athens. He was also a fellow of the American Academy of Arts and Sciences; a member of the German Archaeological Institute; a corresponding member of the American Institute of Architects; a member of the Architectural League of New York; a member of the Commission des Musees royaux des Beaux Arts de Belgique, and of many other learned societies. While in Boston Robinson served for eight years as secretary of the art commission of the city of Boston. He selected and arranged the collection of casts of classical and renaissance sculpture in the Slater Memorial Museum at Norwich, Connecticut, and also formed the collection of casts in the Metropolitan Museum. In 1893-94 and from 1898 to 1902 he was lecturer in classical archaeology at Harvard University. His catalogues of Greek and Roman casts and Greek, Etruscan, and Roman vases in the Boston Museum, as well as scholarly publications in the annual reports, were of value to scholars and students alike. After taking up work in New York, his administrative duties restricted his writing to short articles, appearing chiefly in the Bulletin of the Metropolitan Museum. In recognition of his long and varied service to the world of art numerous degrees and foreign orders were conferred upon him.
Member of the Council of the Archaeological Institute of America and president of its New York society;
Member of the managing committee of the American School of Classical Studies in Athens;
Trustee of the American Academy in Rome;
Member of the Executive Committee of the American Society for the Excavation of Sardis;
Director of the American Federation of Arts;
Trustee of the Museum of the City of New York;
Member of the Commission for the Excavation of the Agora of Athens.
Fellow of the American Academy of Arts and Sciences;
Member of the German Archaeological Institute; Corresponding member of the American Institute of Architects;
Member of the Architectural League of New York;
Member of the Commission des Musees royaux des Beaux Arts de Belgique, and of many other learned societies.
In 1881 he married Elizabeth H. Gould, of Boston, and a son was born in 1882.