| 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 |
| Sir Hubert Henderson FBA | Year of birth 1890 | Year of death 1952 | Year elected 1948 | Fellowship category UK |
| Professor Dr Martin Hengel FBA | Year of birth 1926 | Year of death 2009 | Year elected 1975 | Fellowship category Corresponding |
| Professor Walter Henning FBA | Year of birth 1908 | Year of death 1967 | Year elected 1954 | Fellowship category UK |
| Professor Louis Henry FBA | Year of birth 1900 | Year of death 1991 | Year elected 1972 | Fellowship category Corresponding |
| Professor Sir Bob Hepple QC, FBA | Year of birth 1934 | Year of death 2015 | Year elected 2003 | Fellowship category UK Emeritus |