Between about 55.5 and 52 million years ago, Earth experienced a series of sudden and extreme global warming events (hyperthermals) superimposed on a long-term warming trend1. The first and largest of these events, the Palaeocene–Eocene Thermal Maximum (PETM), is characterized by a massive input of carbon, ocean acidification2 and an increase in global temperature of about 5 °C within a few thousand years3. Although various explanations for the PETM have been proposed4,5,6, a satisfactory model that accounts for the source, magnitude and timing of carbon release at the PETM and successive hyperthermals remains elusive. Here we use a new astronomically calibrated cyclostratigraphic record from central Italy7 to show that the Early Eocene hyperthermals occurred during orbits with a combination of high eccentricity and high obliquity. Corresponding climate–ecosystem–soil simulations accounting for rising concentrations of background greenhouse gases8 and orbital forcing show that the magnitude and timing of the PETM and subsequent hyperthermals can be explained by the orbitally triggered decomposition of soil organic carbon in circum-Arctic and Antarctic terrestrial permafrost. This massive carbon reservoir had the potential to repeatedly release thousands of petagrams (1015 grams) of carbon to the atmosphere–ocean system, once a long-term warming threshold had been reached just before the PETM. Replenishment of permafrost soil carbon stocks following peak warming probably contributed to the rapid recovery from each event9, while providing a sensitive carbon reservoir for the next hyperthermal10. As background temperatures continued to rise following the PETM, the areal extent of permafrost steadily declined, resulting in an incrementally smaller available carbon pool and smaller hyperthermals at each successive orbital forcing maximum. A mechanism linking Earth’s orbital properties with release of soil carbon from permafrost provides a unifying model accounting for the salient features of the hyperthermals.