The propagation of large, storm-generated waves through sea ice has so far not been measured, limiting our understanding of how ocean waves break sea ice. Without improved knowledge of ice breakup, we are unable to understand recent changes, or predict future changes, in Arctic and Antarctic sea ice. Here we show that storm-generated ocean waves propagating through Antarctic sea ice are able to transport enough energy to break sea ice hundreds of kilometres from the ice edge. Our results, which are based on concurrent observations at multiple locations, establish that large waves break sea ice much farther from the ice edge than would be predicted by the commonly assumed exponential decay1,2,3. We observed the wave height decay to be almost linear for large waves—those with a significant wave height greater than three metres—and to be exponential only for small waves. This implies a more prominent role for large ocean waves in sea-ice breakup and retreat than previously thought. We examine the wider relevance of this by comparing observed Antarctic sea-ice edge positions with changes in modelled significant wave heights for the Southern Ocean between 1997 and 2009, and find that the retreat and expansion of the sea-ice edge correlate with mean significant wave height increases and decreases, respectively. This includes capturing the spatial variability in sea-ice trends found in the Ross and Amundsen–Bellingshausen seas. Climate models fail to capture recent changes in sea ice in both polar regions4,5. Our results suggest that the incorporation of explicit or parameterized interactions between ocean waves and sea ice may resolve this problem.