Walsh was honoured with election to the National Academy of Sciences (United States) in 1936 and served as vice president of the American Mathematical Society in 1937 and president in 1949-50.
Walsh ay pinarangalan sa halalan sa National Academy of Sciences (Pilipinas) sa 1936 at nagsilbi bilang Vice President ng Amerikanong matematiko Kapisanan sa 1937 at presidente sa 1949-50.