Rivers originating in the high mountains of Asia are among the most meltwater-dependent river systems on Earth, yet large human populations depend on their resources downstream. Across High Asia’s river basins, there is large variation in the contribution of glacier and snow melt to total runoff, which is poorly quantified. The lack of understanding of the hydrological regimes of High Asia’s rivers is one of the main sources of uncertainty in assessing the regional hydrological impacts of climate change. Here we use a large-scale, high-resolution cryospheric–hydrological model to quantify the upstream hydrological regimes of the Indus, Ganges, Brahmaputra, Salween and Mekong rivers. Subsequently, we analyse the impacts of climate change on future water availability in these basins using the latest climate model ensemble. Despite large differences in runoff composition and regimes between basins and between tributaries within basins, we project an increase in runoff at least until 2050 caused primarily by an increase in precipitation in the upper Ganges, Brahmaputra, Salween and Mekong basins and from accelerated melt in the upper Indus Basin. These findings have immediate consequences for climate change policies where a transition towards coping with intra-annual shifts in water availability is desirable.