Corson was born in Philadelphia, Pennsylvania. He held a position in the library of the Smithsonian Institution, Washington, D.C. (1849-1856), was a lecturer on English literature in Philadelphia (1859-1865), and was professor of English at Girard College, Philadelphia (1865-1866), and in St. Johns College, Annapolis, Maryland (1866-1870). In 1870-1871 he was professor of rhetoric and oratory at Cornell University, where he was professor of Anglo-Saxon and English literature (1872-1886), of English literature and rhetoric (1886-1890), and from 1890 to 1903 (when he became professor emeritus) of English literature, a chair formed for him. His papers are held at Cornell University.
- Chaucer's Legende of Goode Women (editor). 1863.
- An Elocutionary Manual. Charles Desilver. 1864.
- Satires of Juvenal (translator). 1868.
- A Hand-Book of Anglo-Saxon and Early English. Holt & Williams. 1871.
- Jottings on the Text of Macbeth. 1874.
- The University of the Future. 1875.
- An introduction to the study of Robert Browning's poetry. D.C. Heath & Co. 1886 or 1889. Check date values in:
- An Introduction to the Study of William Shakespeare. D.C. Heath & Co. 1889.
- A Primer of English Verse. Ginn. 1893.
- The Aims of Literary Study. 1895.
- The Voice and Spiritual Education. 1896.
- Selections from Chaucer's Canterbury Tales (editor). 1896.
- An Introduction to the Study of Milton. 1899.
- The voice and spiritual education. Macmillan. 1904.
He edited a translation by his wife, Caroline Rollin (d. 1901), of Pierre Janet's Mental State of Hystericals (1901).
- George Norman Highley, ed. The Corson family: a history of the descendants of Benjamin Corson, son of Cornelius Corssen of Staten Island, New York, H.L. Everett, 1906.
- Chisholm, Hugh, ed. (1911). "Corson, Hiram". Encyclopædia Britannica (11th ed.). Cambridge University Press.