Radiative effects of anthropogenic changes in atmospheric composition are expected to cause climate changes, in particular an intensification of the global water cycle with a consequent increase in flood risk. But the detection of anthropogenically forced changes in flooding is difficult because of the substantial natural variability; the dependence of streamflow trends on flow regime further complicates the issue. Here we investigate the changes in risk of great floods - that is, floods with discharges exceeding 100-year levels from basins larger than 200,000 km2 - using both streamflow measurements and numerical simulations of the anthropogenic climate change associated with greenhouse gases and direct radiative effects of sulphate aerosols. We find that the frequency of great floods increased substantially during the twentieth century. The recent emergence of a statistically significant positive trend in risk of great floods is consistent with results from the climate model, and the model suggests that the trend will continue.