The air–sea transfer of heat and fresh water plays a critical role in the global climate system1. This is particularly true for the Greenland and Iceland seas, where these fluxes drive ocean convection that contributes to Denmark Strait overflow water, the densest component of the lower limb of the Atlantic Meridional Overturning Circulation (AMOC; ref. 2). Here we show that the wintertime retreat of sea ice in the region, combined with different rates of warming for the atmosphere and sea surface of the Greenland and Iceland seas, has resulted in statistically significant reductions of approximately 20% in the magnitude of the winter air–sea heat fluxes since 1979. We also show that modes of climate variability other than the North Atlantic Oscillation (NAO; refs 3, 4, 5, 6, 7) are required to fully characterize the regional air–sea interaction. Mixed-layer model simulations imply that further decreases in atmospheric forcing will exceed a threshold for the Greenland Sea whereby convection will become depth limited, reducing the ventilation of mid-depth waters in the Nordic seas. In the Iceland Sea, further reductions have the potential to decrease the supply of the densest overflow waters to the AMOC.