Sediment storage is an often-neglected term in sediment budgets, despite being the crucial link between rates of erosion and sediment yield. Mountain belts in particular host large valley fills that modulate fluxes of water and sediment, buffer the geomorphic coupling between hillslopes and river channels, reduce local valley relief, and protect bedrock from fluvial incision. Here we propose a region-growing algorithm based on a slope-gradient criterion to automatically extract areas of postglacial fluvial and lacustrine valley fills from digital topography at the mountain-belt scale. Applying this method to the European Alps, we find that the size-frequency relationship of 17,766 individual sediment storage units, expressed by either area or volume, follows a power law over four and five orders of magnitude with scaling exponents -1.77 and -1.71, respectively. We show that 90% of the area covered by sediment storage is in the lower quartile of the mountain belt's elevation and below the median local relief. On average, low-gradient valley fill occupies 6% of the studied drainage basins. This fraction increases with basin size, likely reflecting the larger accommodation space of trunk valleys generated by multiple glacial-interglacial cycles. Comparison with sediment storage mapped in the Southern Alps, New Zealand, indicates that rates of uplift and precipitation control the extent and spatial distribution of sediment storage at the mountain-belt scale.