Pronounced climate changes have occurred since the 1970s, including rapid loss of Arctic sea ice, large-scale warming and increased tropical storm activity in the Atlantic. Anthropogenic radiative forcing is likely to have played a major role in these changes, but the relative influence of anthropogenic forcing and natural variability is not well established. The above changes have also occurred during a period in which the North Atlantic Oscillation has shown marked multidecadal variations. Here we investigate the role of the North Atlantic Oscillation in these rapid changes through its influence on the Atlantic meridional overturning circulation and ocean heat transport. We use climate models to show that observed multidecadal variations of the North Atlantic Oscillation can induce multidecadal variations in the Atlantic meridional overturning circulation and poleward ocean heat transport in the Atlantic, extending to the Arctic. Our results suggest that these variations have contributed to the rapid loss of Arctic sea ice, Northern Hemisphere warming, and changing Atlantic tropical storm activity, especially in the late 1990s and early 2000s. These multidecadal variations are superimposed on long-term anthropogenic forcing trends that are the dominant factor in long-term Arctic sea ice loss and hemispheric warming.