The onset of major glaciations in the Northern Hemisphere about 2.7 million years ago was most probably induced by climate cooling during the late Pliocene epoch. These glaciations, during which the Northern Hemisphere ice sheets successively expanded and retreated, are superimposed on this long-term climate trend, and have been linked to variations in the Earth's orbital parameters. One intriguing problem associated with orbitally driven glacial cycles is the transition from 41,000-year to 100,000-year climatic cycles that occurred without an apparent change in insolation forcing. Several hypotheses have been proposed to explain the transition, both including and excluding ice-sheet dynamics. Difficulties in finding a conclusive answer to this palaeoclimatic problem are related to the lack of sufficiently long records of ice-sheet volume or sea level. Here we use a comprehensive ice-sheet model and a simple ocean-temperature model to extract three-million-year mutually consistent records of surface air temperature, ice volume and sea level from marine benthic oxygen isotopes. Although these records and their relative phasings are subject to considerable uncertainty owing to limited availability of palaeoclimate constraints, the results suggest that the gradual emergence of the 100,000-year cycles can be attributed to the increased ability of the merged North American ice sheets to survive insolation maxima and reach continental-scale size. The oversized, wet-based ice sheet probably responded to the subsequent insolation maximum by rapid thinning through increased basal-sliding, thereby initiating a glacial termination. Based on our assessment of the temporal changes in air temperature and ice volume during individual glacials, we demonstrate the importance of ice dynamics and ice-climate interactions in establishing the 100,000-year glacial cycles, with enhanced North American ice-sheet growth and the subsequent merging of the ice sheets being key elements.