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During the last glacial period, the Northern Hemisphere climate underwent dramatic swings between relatively warm periods and cold periods—the Dansgaard–Oeschger oscillations. Here, we use recent progress in our theoretical understanding of the Atlantic meridional overturning circulation to develop a simple predictive model that relates variations in the overturning circulation to rapid changes in North Atlantic sea ice and the gradual recharge and discharge of the deep ocean temperature. The robustness of the model is tested against results from idealized general circulation model simulations, and exploration of its parameter space provides insights into the mechanisms dictating the overturning circulation’s response to atmospheric forcing variations. The theoretical model predicts that global atmospheric temperature and salinity fluxes control the relative length of stadial versus interstadial conditions and reproduces the evolving characteristics of theδ¹⁸O isotope ice core record over the last 100 kyr when forced only by the slowly changing global mean temperature. The findings indicate that the prominent climate variability observed in the Greenland ice cores is directly influenced by the gradual evolution of global temperatures and salinity fluxes. This variability can be attributed to a relatively simple physical mechanism that involves the interplay of fast positive sea ice and salt-advection feedbacks, along with a delayed negative deep-ocean-temperature feedback.