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Eliot was born in Boston, the son of William Havard Eliot (1796 - 1831) and Margaret Boies (Bradford) Eliot, and the grandson of banker Samuel Eliot. His father built the Tremont House, participated in the musical life of the city, had variants of his names including Hayward, Harvard, Havard, Howard, and Elliott, and died suddenly in 1831 while campaigning for mayor. His mother was a daughter of Alden Bradford and granddaughter of Harrison Gray Otis. Charles Eliot Norton was Eliot's cousin.
Eliot graduated first in the class of 1839 at Harvard College and, after two years in a counting house in Boston, toured for four years in Europe in the early 1840s. During the decade following his return, he devoted himself to writing. However, on June 7, 1853, Eliot married Emily Marshall Otis (1832-1906) of Boston, and his writing career gradually drew to a close. Their daughter, Emily Marshall Eliot Morison, was the mother of noted historian Samuel Eliot Morison (1887–1976).
In 1856, Eliot became professor of history and political science at Trinity College in Hartford, Connecticut, and then served as Trinity's president from 1860-1864. In 1864 Eliot returned to Boston, though he continued to teach classes at Trinity until 1874. At Harvard, he was an overseer from 1866 to 1872 and a lecturer in history from 1870-1873. He also served from 1868-1872 as president of the American Social Science Association. From 1872-1876 he served as headmaster of the Boston Girls' High and Normal School, and from 1878-1880 as superintendent of Boston Public Schools, later serving from 1885-1888 on the Boston School Committee.
Eliot was a trustee of Massachusetts General Hospital and of the Massachusetts School for the Feeble-Minded, and for 26 years a member and president of the board of trustees of the Perkins Institute for the Blind. He was also active as a trustee, director, etc., for Museum of Fine Arts, Boston, the Boston Athenaeum, the American Academy of Arts and Sciences, the Massachusetts Bible Society, and the Massachusetts Historical Society.
- Translations from the Spanish Poet José Zorilla, (1846).
- Passages from the History of Liberty, (1847).
- The Liberty of Rome, (2 volumes, 1849) which was revised to form Part I of the History of Liberty: Part I, The Ancient Romans; Part II, The Early Christians, (4 volumes, 1853).
- Manual of United States History: From 1492 to 1850, (1856).
- Manual of the United States: From 1492 to 1872, (1874).
- Poetry for Children, (1879).
- Selections from American Authors: A Reading Book for School and Home, (1879).
- The Arabian Nights' Entertainments: Six Stories, (1880).