Abrupt cooling is observed at the end of interglacials in many paleoclimate records, but the mechanism responsible remains unclear. Using model simulations, we demonstrate that there exists a threshold in the level of astronomically induced insolation below which abrupt changes at the end of interglacials of the past 800,000 years occur. When decreasing insolation reaches the critical value, it triggers a strong, abrupt weakening of the Atlantic meridional overturning circulation and a cooler mean climate state accompanied by high-amplitude variations lasting for several thousand years. The mechanism involves sea ice feedbacks in the Nordic and Labrador Seas. The ubiquity of this threshold suggests its fundamental role in terminating the warm climate conditions at the end of interglacials.