Hess was born in New York City and educated at Yale, graduating in 1927, and Princeton where he gained his PhD in 1932. He worked first as a field geologist in Northern Rhodesia (now Zambia) in the period 1928–29. After a year at Rutgers in 1932 he moved to Princeton in 1934, becoming professor of geology in 1948.

Hess was a key figure in the postwar revolution in the Earth sciences. He was the first to draw up theories using the considerable discoveries on the nature of the ocean floor that were made in the postwar period. Hess himself discovered about 160 flat-topped summits on the ocean bed, which he named ‘guyots’ for an earlier Princeton geologist, Arnold Guyot. As they failed to produce atolls he dated them to the Precambrian, 600 million years ago, before the appearance of corals. But in 1956 Cretaceous fossils, from only 100 million years ago, were found in Pacific guyots. The whole of the ocean floor was discovered to be surprisingly young, dating only as far back as the Mesozoic, while the continental rocks were much older.

In 1962 Hess published his important paper, History of Ocean Basins. The ocean floors were young, he argued, as they were constantly being renewed by magma flowing from the mantle up through the oceanic rifts, discovered by William Morris Ewing, and spreading out laterally. This became known as the sea-floor spreading hypothesis and was a development of the convection-currents theory proposed by Arthur Holmes in 1929. The hypothesis has been modified since its proposal, notably through the work of Drummond Hoyle Matthews and Frederick Vine on magnetic anomalies, but remains largely accepted.