Precipitation changes projected for the end of the twenty-first century show an increase of more than 50 per cent in the Arctic regions. This marked increase, which is among the highest globally, has previously been attributed primarily to enhanced poleward moisture transport from lower latitudes. Here we use state-of-the-art global climate models to show that the projected increases in Arctic precipitation over the twenty-first century, which peak in late autumn and winter, are instead due mainly to strongly intensified local surface evaporation (maximum in winter), and only to a lesser degree due to enhanced moisture inflow from lower latitudes (maximum in late summer and autumn). Moreover, we show that the enhanced surface evaporation results mainly from retreating winter sea ice, signalling an amplified Arctic hydrological cycle. This demonstrates that increases in Arctic precipitation are firmly linked to Arctic warming and sea-ice decline. As a result, the Arctic mean precipitation sensitivity (4.5 per cent increase per degree of temperature warming) is much larger than the global value (1.6 to 1.9 per cent per kelvin). The associated seasonally varying increase in Arctic precipitation is likely to increase river discharge and snowfall over ice sheets (thereby affecting global sea level), and could even affect global climate through freshening of the Arctic Ocean and subsequent modulations of the Atlantic meridional overturning circulation.