According to the Milankovitch theory, changes in summer insolation in the high-latitude Northern Hemisphere caused glacial cycles through their impact on ice-sheet mass balance1. Statistical analyses of long climate records supported this theory, but they also posed a substantial challenge by showing that changes in Southern Hemisphere climate were in phase with or led those in the north2. Although an orbitally forced Northern Hemisphere signal may have been transmitted to the Southern Hemisphere3, insolation forcing can also directly influence local Southern Hemisphere climate, potentially intensified by sea-ice feedback4, 5, 6, suggesting that the hemispheres may have responded independently to different aspects of orbital forcing. Signal processing of climate records cannot distinguish between these conditions, however, because the proposed insolation forcings share essentially identical variability7. Here we use transient simulations with a coupled atmosphere–ocean general circulation model to identify the impacts of forcing from changes in orbits, atmospheric CO2 concentration, ice sheets and the Atlantic meridional overturning circulation (AMOC) on hemispheric temperatures during the first half of the last deglaciation (22–14.3 kyr bp). Although based on a single model, our transient simulation with only orbital changes supports the Milankovitch theory in showing that the last deglaciation was initiated by rising insolation during spring and summer in the mid-latitude to high-latitude Northern Hemisphere and by terrestrial snow–albedo feedback. The simulation with all forcings best reproduces the timing and magnitude of surface temperature evolution in the Southern Hemisphere in deglacial proxy records8, 9. AMOC changes associated with an orbitally induced retreat of Northern Hemisphere ice sheets10 is the most plausible explanation for the early Southern Hemisphere deglacial warming and its lead over Northern Hemisphere temperature; the ensuing rise in atmospheric CO2 concentration provided the critical feedback on global deglaciation9, 11.