Water plays a first-order role in basal sliding of glaciers and ice sheets and is often a key constituent of accelerated glacier motion. Subglacial water is known to occupy systems of cavities and conduits at the interface between ice and the underlying bed surface, depending upon the history of water input and the characteristics of the substrate. Full understanding of the extent and configuration of basal water is lacking, however, because direct observation is difficult. This limits our ability to simulate ice dynamics and the subsequent impacts on sea-level rise realistically. Here we show that the subglacial hydrological system can have a large volume of water occupying basal crevasses that extend upward from the bed into the overlying ice. Radar and seismic imaging combined with in situ borehole measurements collected on Bench Glacier, Alaska, reveal numerous water-filled basal crevasses with highly transmissive connections to the bed. Some crevasses extend many tens of metres above the bed and together they hold a volume of water equivalent to at least a decimetre layer covering the bed. Our results demonstrate that the basal hydrologic system can extend high into the overlying ice mass, where basal crevasses increase water-storage capacity and could potentially modulate basal water pressure. Because basal crevasses can form under commonly observed glaciological conditions, our findings have implications for interpreting and modelling subglacial hydrologic processes and related sliding accelerations of glaciers and ice sheets.