Clouds substantially affect Earth's energy budget by reflecting solar radiation back to space and by restricting emission of thermal radiation to space. They are perhaps the largest uncertainty in our understanding of climate change, owing to disagreement among climate models and observational datasets over what cloud changes have occurred during recent decades and will occur in response to global warming. This is because observational systems originally designed for monitoring weather have lacked sufficient stability to detect cloud changes reliably over decades unless they have been corrected to remove artefacts. Here we show that several independent, empirically corrected satellite records exhibit large-scale patterns of cloud change between the 1980s and the 2000s that are similar to those produced by model simulations of climate with recent historical external radiative forcing. Observed and simulated cloud change patterns are consistent with poleward retreat of mid-latitude storm tracks, expansion of subtropical dry zones, and increasing height of the highest cloud tops at all latitudes. The primary drivers of these cloud changes appear to be increasing greenhouse gas concentrations and a recovery from volcanic radiative cooling. These results indicate that the cloud changes most consistently predicted by global climate models are currently occurring in nature.