He was regent of the Smithsonian Institution, as well as professor of Greek literature and president of Harvard University.

Greece, Ancient and Modern (2 vols., 1867), forty-nine lectures before the Lowell Institute, is scholarly, able and suggestive of the author's personality.

Among his miscellaneous publications are the American edition of Sir William Smith's History of Greece (1855); translations of Menzel's German Literature (1840), of Munk's Metres of the Greeks and Romans (1844), and of Guyot's Earth and Man (1849); and Familiar Letters from Europe (1865).

He died of "disease of the heart" while at his brother's house in Chester, Pennsylvania, en route to a meeting of the Smithsonian Institution in Washington, D.C.[5][3] He was buried at Mount Auburn Cemetery.

A historical marker in the town of West Newbury marks Felton's birthplace.