Various transboundary river basins are facing increased pressure on water resources in near future. However, little is known ab out the future drivers globally, namely, changes in natural local runoff and natural inflows from upstream parts of a basin, as well as local and upstream water consumption. Here we use an ensemble of four global hydrological models forced by five global climate models and the latest greenhouse‐gas concentration (RCP) and socioeconomic pathway (SSP) scenarios to assess the impact of these drivers on transboundary water stress in the past and future. Our results show that population under water stress is expected to increase by 50% under a low population growth and emissions scenario (SSP1‐RCP2.6) and double under a high population growth and emission scenario (SSP3‐RCP6.0), compared to the year 2010. As changes in water availability have a smaller effect when water is not yet scarce, changes in water stress globally are dominated by local water consumption—managing local demand is thus necessary in order to avoid future stress. Focusing then on the role of upstream changes, we identified upstream availability (i.e., less natural runoff or increased water consumption) as the dominant driver of changes in net water availability in most downstream areas. Moreover, an increased number of people will be living in areas dependent on upstream originating water in 2050. International water treaties and management will therefore have an increasingly crucial role in these hot spot regions to ensure fair management of transboundary water resources.