Supraglacial debris strongly modulates glacier melt rates and can be decisive for ice dynamics and mountain hydrology. It is ubiquitous in High-Mountain Asia, yet because its thickness and supply rate from local topography are poorly known, our ability to forecast regional glacier change and streamflow is limited. Here we combined remote sensing and numerical modelling to resolve supraglacial debris thickness by altitude for 4689 glaciers in High-Mountain Asia, and debris-supply rate to 4141 of those glaciers. Our results reveal extensively thin supraglacial debris and high spatial variability in both debris thickness and supply rate. Debris-supply rate increases with the temperature and slope of debris-supply slopes regionally, and debris thickness increases as ice flow decreases locally. Our centennial-scale estimates of debris-supply rate are typically an order of magnitude or more lower than millennial-scale estimates of headwall-erosion rate from Beryllium-10 cosmogenic nuclides, potentially reflecting episodic debris supply to the region’s glaciers.