Distributed acoustic sensing (DAS) is a new technology in which seismic energy is recorded at high spatial and temporal resolution along a fibre-optic cable. We show analyses from the first glaciological borehole deployment of DAS to measure the englacial and subglacial seismic properties of Store Glacier, a fast-flowing outlet of the Greenland Ice Sheet. By characterizing compressional and shear wave propagation in 1030 m-deep vertical seismic profiles, sampled at 10 m vertical resolution, we detected a transition from isotropic to anisotropic ice consistent with a Holocene-Wisconsin transition at 83% of the ice thickness. We also infer temperate ice in the lowermost 100 m of the glacier, and identified subglacial reflections originating from the base of a 20 m-thick layer of consolidated sediment. Our findings highlight the transformative potential of DAS to inform the physical properties of glaciers and ice sheets.