Osborn was born in Fairfield, Connecticut, and studied at Princeton University. He was professor of comparative anatomy from 1883 to 1890 at Princeton. In 1891 he was hired jointly by Columbia University and the American Museum of Natural History, New York. He became professor of biology at Columbia University, becoming professor of zoology in 1896. At the museum he succeeded Morris K. Jesup as president in 1908, serving until 1933, during which time he accumulated one of the finest fossil collections in the world He assembled a great team of fossil hunters and preparators, which included Roy Chapman Andrews, one of the prototypes of Indiana Jones, and Charles R. Knight, who made murals of dinosaurs in their habitats and sculptures of the living creatures.
He was mentored by the paleontologist Edward Drinker Cope, whom he met on a fossil-hunting expedition in Wyoming . The articulate Fairfield Osborne joined the US Geological Survey in 1900 and became senior vertebrate paleontologist in 1924. He led many fossil-hunting expeditions into the American Southwest, starting with his first to Colorado and Wyoming in 1877, when he met Cope. He described and named Ornitholestes in 1903, Tyrannosaurus rex in 1905, the Pentaceratops in 1923, and the Velociraptor in 1924.
Some of his contributions are less celebrated: Osborn's belief in the now-discredited idea of orthogenesis is one such contribution, his promotion of eugenics, another. Andrews' explorations in the Gobi Desert were in part set in action by Osborn's certainty that the origins of man were to be found in Asia. His unfortunate Man Rises to Parnassus, built on the misleading, but "almost miraculous" Piltdown Man hoax, reveals the deeply-imbedded racialism of even the educated classes of his generation, supported on pseudoscience.
His best known publication might be his two-volume work of 1936, The Proboscidea: A Monograph of the Discovery, Evolution, Migration and Extinction of the Mastodonts and Elephants of the World, in which he discussed the fossil history and evolution of elephants and their relatives. A second volume appeared in 1942, after his death. He published many papers on fossil proboscideans during his career.
Osborn wrote an influential textbook, The Age of Mammals in Asia, Europe and North America (1910). He also authored, The Origin and Evolution of Life (1916).
He co-founded the Save-the-Redwoods League in 1918. He was long-time president of the New York Zoological Society.
He was the father of the conservationist and naturalist Henry Fairfield Osborn, Jr.