Anthropogenic climate change is expected to affect global river flow. Here, we analyze time series of low, mean, and high river flows from 7250 observatories around the world covering the years 1971 to 2010. We identify spatially complex trend patterns, where some regions are drying and others are wetting consistently across low, mean, and high flows. Trends computed from state-of-the-art model simulations are consistent with the observations only if radiative forcing that accounts for anthropogenic climate change is considered. Simulated effects of water and land management do not suffice to reproduce the observed trend pattern. Thus, the analysis provides clear evidence for the role of externally forced climate change as a causal driver of recent trends in mean and extreme river flow at the global scale.