During the last 20,000 years the climate of the earth has changed from a state much colder than today with large ice sheets in North America and Northwest Eurasia to its present state. The fully-interactive simulation of this transition represents a hitherto unsolved challenge for state-of-the-art climate models. We use a novel coupled comprehensive atmosphere–ocean–vegetation-ice sheet–solid earth model to simulate the transient climate evolution from the last glacial maximum to preindustrial times. The model considers dynamical changes of the glacier mask, land–sea mask and river routing. An ensemble of transient model simulations successfully captures the main features of the last deglaciation, as depicted by proxy estimates. In addition, our model simulates a series of abrupt climate changes, which can be attributed to different drivers. Abrupt cooling events during the glacial and the first half of the deglaciation are caused by Heinrich-event like ice-sheet surges, which are part of the model generated internal variability. We show that the timing of these surges depends on the initial state and the model parameters. Abrupt events during the second half of the deglaciation are caused by a long-term shift in the sign of the Arctic freshwater budget, changes in river routing and/or the opening of ocean passages.