Climate changes are pronounced in Arctic regions and increase the vulnerability of the Arctic coastal zone. For example, increases in melting of the Greenland Ice Sheet and reductions in sea ice and permafrost distribution are likely to alter coastal morphodynamics. The deltas of Greenland are largely unaffected by human activity, but increased freshwater runoff and sediment fluxes may increase the size of the deltas, whereas increased wave activity in ice-free periods could reduce their size, with the net impact being unclear until now. Here we show that southwestern Greenland deltas were largely stable from the 1940s to 1980s, but prograded (that is, sediment deposition extended the delta into the sea) in a warming Arctic from the 1980s to 2010s. Our results are based on the areal changes of 121 deltas since the 1940s, assessed using newly discovered aerial photographs and remotely sensed imagery. We find that delta progradation was driven by high freshwater runoff from the Greenland Ice Sheet coinciding with periods of open water. Progradation was controlled by the local initial environmental conditions (that is, accumulated air temperatures above 0 °C per year, freshwater runoff and sea ice in the 1980s) rather than by local changes in these conditions from the 1980s to 2010s at each delta. This is in contrast to a dominantly eroding trend of Arctic sedimentary coasts along the coastal plains of Alaska, Siberia and western Canada, and to the spatially variable patterns of erosion and accretion along the large deltas of the main rivers in the Arctic. Our results improve the understanding of Arctic coastal evolution in a changing climate, and reveal the impacts on coastal areas of increasing ice mass loss and the associated freshwater runoff and lengthening of open-water periods.