Sea-level fluctuations of about 20-30m occurred throughout the last glacial period. These fluctuations seem to have been derived primarily from changes in the volume of Northern Hemisphere ice sheets, and cannot be attributed solely to ice melt caused by varying solar radiation. Here we use a fully coupled climate model to show that the transport of relatively fresh Pacific water into the North Atlantic Ocean was limited when lower sea level restricted or closed the Bering Strait, resulting in saltier North Atlantic surface waters. This invigorated deep convection in the North Atlantic Ocean, strengthening meridional overturning circulation and northward heat transport in our model, which consequently promoted melting of ice sheets in North America and Europe. Our simulations show that the associated sea-level rise led to a reopening of the Bering Strait; the flux of relatively fresh water into the North Atlantic Ocean muted meridional overturning circulation and led to cooling and ice-sheet advance in the Northern Hemisphere. We conclude that the repetition of this cycle could produce the sea-level changes that have been observed throughout the last glacial cycle.