In recent decades, meltwater runoff has accelerated to become the dominant mechanism for mass loss in the Greenland ice sheet(1-3). In Greenland's high-elevation interior, porous snow and firn accumulate; these can absorb surface meltwater and inhibit runoff(4), but this buffering effect is limited if enough water refreezes near the surface to restrict percolation(5,6). However, the influence of refreezing on runoff from Greenland remains largely unquantified. Here we use firn cores, radar observations and regional climate models to show that recent increases in meltwater have resulted in the formation of metres-thick, low-permeability 'ice slabs' that have expanded the Greenland ice sheet's total runoff area by 26 +/- 3 per cent since 2001. Although runoff from the top of ice slabs has added less than one millimetre to global sea-level rise so far, this contribution will grow substantially as ice slabs expand inland in a warming climate. Runoff over ice slabs is set to contribute 7 to 33 millimetres and 17 to 74 millimetres to global sea-level rise by 2100 under moderate-and high-emissions scenarios, respectively-approximately double the estimated runoff from Greenland's high-elevation interior, as predicted by surface mass balance models without ice slabs. Ice slabs will have an important role in enhancing surface meltwater feedback processes, fundamentally altering the ice sheet's present and future hydrology.