The glacierized Tien Shan - Pamir - Karakoram mountain complex supplies water to about 42 million people. Yet, the knowledge about future glacial runoff in response to future climate is limited. Here, we address this issue using a hydrological model, that includes the three components of glacial runoff: ice melt, snowmelt and the runoff of rainfall over ice. The model is forced by climate projections of the CMIP5 models. We find that the three components exhibit different long-term trajectories, sometimes opposite in sign to the long-term trend in glacier impacts. For the eastern slope basins, streamflow is projected to increase by 28% (ranging from 9 to 44%, from climate model variation (CMV)) by the late 21st century, under the representative concentration pathway, RCP8.5. Ice melt contributes 39% (25 to 65%, CMV) of the total streamflow increase. However, streamflow from the western slopes is projected to decrease by 5% (-24 to 16%, CMV), due to the smaller contribution of ice melt, less precipitation and higher evapotranspiration. Increasing water supply from the eastern slopes suggests more water availability for currently degraded downstream ecosystems in the Xinjiang province of China, while the likely decreasing streamflow in Central Asian rivers on the western slopes indicates new regulations will be needed.