| Professor Friedrich Hayek CH, FBA | Year of birth 1899 | Year of death 1992 | Year elected 1944 | Fellowship category UK |
| Professor Jack Hayward FBA | Year of birth 1931 | Year of death 2017 | Year elected 1990 | Fellowship category UK Emeritus |
| Professor John N Hazard FBA | Year of birth 1900 | Year of death 1995 | Year elected 1973 | Fellowship category Corresponding |
| Professor Harold Dexter Hazeltine FBA | Year of birth 1871 | Year of death 1960 | Year elected 1924 | Fellowship category UK |
| Professor Patsy Healey FBA | Year of birth None | Year of death 2024 | Year elected 2009 | Fellowship category UK Emeritus |
| Professor Seamus Heaney FBA | Year of birth 1939 | Year of death 2013 | Year elected 1999 | Fellowship category Corresponding |
| Sir Thomas Heath KCB, KCVO, FBA | Year of birth 1861 | Year of death 1940 | Year elected 1932 | Fellowship category UK |
| Professor Herbert Heaton FBA | Year of birth 1870 | Year of death 1973 | Year elected 1967 | Fellowship category Corresponding |
| Professor Johan Ludvig Heiberg FBA | Year of birth 1854 | Year of death 1928 | Year elected 1904 | Fellowship category Corresponding |
| Professor Hermann Heimpel FBA | Year of birth 1901 | Year of death 1988 | Year elected 1986 | Fellowship category Corresponding |
| Professor Dr Walther Heissig FBA | Year of birth 1913 | Year of death 2005 | Year elected 1988 | Fellowship category Corresponding |
| Professor Julius Held FBA | Year of birth 1905 | Year of death 2002 | Year elected 1992 | Fellowship category Corresponding |
| Professor Jan Hellner FBA | Year of birth 1917 | Year of death 2002 | Year elected 1991 | Fellowship category Corresponding |
| Professor Carl Hempel FBA | Year of birth 1900 | Year of death 1997 | Year elected 1977 | Fellowship category Corresponding |
| Professor Hugh O'Neill Hencken FBA | Year of birth 1902 | Year of death 1981 | Year elected 1972 | Fellowship category Corresponding |
| Professor Eugénie Henderson FBA | Year of birth 1914 | Year of death 1989 | Year elected 1986 | Fellowship category UK |