A graduate of Yale University (1828), he was made a tutor at that university, but soon afterward he became a teacher in the Hartford grammar school. Becoming slightly deaf, he taught in the American Institution for the Deaf and Dumb at Hartford, Conn. (1830-1832) and at the New York Institution for the Deaf and Dumb (1832-1837).
In 1854, he went to the University of Mississippi, first as a professor of mathematics and astronomy, then as president (1850-1858); and finally as chancellor (1858-1861), resigning when the Civil War began. In 1860 he was a member of the expedition sent to Labrador to observe the solar eclipse. He went to Washington in 1863, as head of the map and chart development of the U.S. Coastal Survey.
In 1864, Barnard returned again to the academic world, this time as president of Columbia University, New York, N.Y., and served in this capacity until his death in 1889. He drew up the plans under which Columbia subsequently developed into a great university. Among his many achievements at Columbia were the introduction of the elective system, the establishment of graduate study, and aid in the founding of Teachers College. Barnard College was named for him. He was a founder of the American Association for the Advancement of Science and of the National Academy of Sciences.