During glacial periods of the Late Pleistocene, an abundance of proxy data demonstrates the existence of large and repeated millennial-scale warming episodes, known as Dansgaard–Oeschger (DO) events1. This ubiquitous feature of rapid glacial climate change can be extended back as far as 800,000 years before present (BP) in the ice core record2, and has drawn broad attention within the science and policy-making communities alike3. Many studies have been dedicated to investigating the underlying causes of these changes, but no coherent mechanism has yet been identified3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Here we show, by using a comprehensive fully coupled model16, that gradual changes in the height of the Northern Hemisphere ice sheets (NHISs) can alter the coupled atmosphere–ocean system and cause rapid glacial climate shifts closely resembling DO events. The simulated global climate responses—including abrupt warming in the North Atlantic, a northward shift of the tropical rainbelts, and Southern Hemisphere cooling related to the bipolar seesaw—are generally consistent with empirical evidence1, 3, 17. As a result of the coexistence of two glacial ocean circulation states at intermediate heights of the ice sheets, minor changes in the height of the NHISs and the amount of atmospheric CO2 can trigger the rapid climate transitions via a local positive atmosphere–ocean–sea-ice feedback in the North Atlantic. Our results, although based on a single model, thus provide a coherent concept for understanding the recorded millennial-scale variability and abrupt climate changes in the coupled atmosphere–ocean system, as well as their linkages to the volume of the intermediate ice sheets during glacials.