Predicting the responses of streamflow to changes in forest management is fundamental to the sustainable regulation of water resources. However, studies of changes in forest cover have yielded unclear and largely unpredictable results. Here we compile a comprehensive and spatially distributed database of forest-management studies worldwide, to assess the factors that control streamflow response to forest planting and removal. We introduce a vegetation-to-bedrock model that includes seven key landscape factors in order to explain the impacts of forest removal and planting on water yield. We show that the amount of water stored in a landscape is the most important factor in predicting streamflow response to forest removal, whereas the loss of water through evaporation and transpiration is the most important factor in predicting streamflow response to forest planting. Our findings affect model parameterizations in climate change mitigation schemes (involving, for example, afforestation or deforestation) in different geologic and climate regions around the world, and inform practices for the sustainable management of water resources.