The Palaeocene–Eocene Thermal Maximum, approximately 55 million years ago, was a period of rapid warming linked to a massive release of carbon to the ocean–atmosphere system1. This warming event was also marked by widespread dissolution of carbonates at the sea floor2. The acidification of deep waters was generally more extensive and severe in the Atlantic and Caribbean, with more modest changes in the Southern and Pacific oceans3, 4, 5. Here we use the UVic ESCM global climate model to show that corrosive deep water spreading from the North Atlantic can explain the spatial variations in carbonate dissolution during the Palaeocene–Eocene Thermal Maximum. In our simulations, highly corrosive waters accumulate in the deep North Atlantic at the onset of the event. Several thousand years after an imposed atmospheric carbon release, warming of the deep ocean destabilizes the North Atlantic water column and triggers deep-water formation. This deep convection causes the corrosive bottom water to spill over an equatorial sill into the South Atlantic. The bottom water then spreads through the Southern and Pacific oceans, progressively gaining alkalinity. We conclude that the pattern of sediment dissolution simulated along the path taken by the corrosive water is consistent with most dissolution estimates from the sediment record.