Claude, who was born at Longlier in Belgium, was educated at the University of Liège where he obtained his doctorate in 1928. He joined the staff of the Rockefeller Institute, New York, in 1929 and in 1941 adopted American citizenship. Claude returned to Belgium in 1948 to serve as director of the Jules Bordet Research Institute, a post he retained until his retirement in 1972.

In the 1930s Claude attempted to purify Peyton Rous's chicken sarcoma virus (RSV) using a centrifuge. He succeeded in producing a fraction with an enhanced sarcogenic power, noting that small granules containing nucleoprotein were present. Suspecting these granules to be the cause of the RSV, he was somewhat surprised to find similar granules present in centrifuged cells taken from uninfected chicken embryo.

Over the next 20 years, using electron microscopes as well as improved centrifuges, Claude began to chart the constitution of the protoplasm. Although the mitochondria had first been described as early as 1897, Claude could distinguish them from what he originally termed ‘microsomes’. Among such microsomes he could make out a lacelike structure spread throughout the cytoplasm, a structure later named the endoplasmic reticulum. Another member of Claude's laboratory, George Palade, went on to identify the ribosome.

For his work in opening up the study of cell structures Claude shared the 1974 Nobel Prize for physiology or medicine with Palade and Christian de Duve.