Surface melt on the Greenland ice sheet has shown increasing trends in areal extent and duration since the beginning of the satellite era. Records for melt were broken in 2005, 2007, 2010 and 2012. Much of the increased surface melt is occurring in the percolation zone, a region of the accumulation area that is perennially covered by snow and firn (partly compacted snow). The fate of melt water in the percolation zone is poorly constrained: some may travel away from its point of origin and eventually influence the ice sheet's flow dynamics and mass balance and the global sea level, whereas some may simply infiltrate into cold snow or firn and refreeze with none of these effects. Here we quantify the existing water storage capacity of the percolation zone of the Greenland ice sheet and show the potential for hundreds of gigatonnes of meltwater storage. We collected in situ observations of firn structure and meltwater retention along a roughly 85-kilometre-long transect of the melting accumulation area. Our data show that repeated infiltration events in which melt water penetrates deeply (more than 10 metres) eventually fill all pore space with water. As future surface melt intensifies under Arctic warming, a fraction of melt water that would otherwise contribute to sea-level rise will fill existing pore space of the percolation zone. We estimate the lower and upper bounds of this storage sink to be 322 ± 44 gigatonnes and  1,289(+388)(-252) gigatonnes, respectively. Furthermore, we find that decades are required to fill this pore space under a range of plausible future climate conditions. Hence, routing of surface melt water into filling the pore space of the firn column will delay expansion of the area contributing to sea-level rise, although once the pore space is filled it cannot quickly be regenerated.