The Indo-Pacific warm pool—the main source of heat and moisture to the global atmosphere—plays a prominent role in tropical and global climate variability. During the Last Glacial Maximum, temperatures within the warm pool were cooler than today and precipitation patterns were altered, but the mechanism responsible for these shifts remains unclear. Here we use a synthesis of proxy reconstructions of warm pool hydrology and a multi-model ensemble of climate simulations to assess the drivers of these changes. The proxy data suggest drier conditions throughout the centre of the warm pool and wetter conditions in the western Indian and Pacific oceans. Only one model out of twelve simulates a pattern of hydroclimate change similar to our reconstructions, as measured by the Cohen’s κ statistic. Exposure of the Sunda Shelf by lower glacial sea level plays a key role in the hydrologic pattern simulated by this model, which results from changes in the Walker circulation driven by weakened convection over the warm pool. We therefore conclude that on glacial–interglacial timescales, the growth and decay of ice sheets exert a first-order influence on tropical climate through the associated changes in global sea level.