Sturgis was a fellow of the American Institute of Architects and of the National Academy of Design; an honorary fellow of the Brooklyn Institute of Arts and Sciences; a fellow in perpetuity of the Metropolitan Museum of Art; life member of the American Numismatic and Archaeological Society; honorary member of the National Society of Mural Painters; and a member of the Architectural League of New York (president in 1889-93), the Grolier Club, the Municipal Art Society, Archaeological Institute of America, National Sculpture Society, the Japan Society, the Fine Arts Federation of New York (first president, 1895–97); member of the University, Century and Players clubs of New York City; and a member of the Society for the Promotion of Hellenic Studies in London.