Assessing the impacts of climate change on water resources of the Congo River Basin (CRB) has attracted widespread interest; however, efforts are hindered by the lack of long-term data availability. Of particular interest to water resource planners and policy makers is the spatiotemporal variability of runoff due to the projected changes in climate. Here, with the aid of a spatially explicit hydrological model forced with precipitation and temperature projections from 25 global climate models (GCMs) under two greenhouse gas emission scenarios, we elucidate the variability in runoff in the near (2016–2035) and mid (2046–2065) 21st century compared to present. Over the equatorial, northern and southwestern CRB, models project an overall increase in precipitation and, subsequently runoff. A decrease in precipitation in the headwater regions of southeastern Congo, leads to a decline in runoff. Climate model selection plays an important role in precipitation projections, for both magnitude and direction of change. Model consensus on the magnitude and the sign (increase or decrease) of change is strong in the equatorial and northern parts of the basin, but weak in the southern basin. The multi-model approach reveals that near-term projections are not impacted by the emission scenarios. However, the mid-term projections depend on the emission scenario. The projected increase in accessible runoff (excluding flood runoff) in most parts of CRB presents new opportunities for augmenting human appropriation of water resources; at the same time, the increase in quick runoff poses new challenges. In the southeast, with the projected decrease, the challenge will be on managing the increasing demands with limited water resources.