Climate change and warming ocean temperatures are a threat to coral reef ecosystems. Since the 1980s, there has been an increase in mass coral bleaching and associated coral mortality due to more frequent and severe thermal stress. Although most research has focused on the role of temperature, coral bleaching is a product of the interacting effects of temperature and other environmental variables such as solar radiation. High light exacerbates the effects of thermal stress on corals, whereas reductions in light can reduce sensitivity to thermal stress. Here, we use an updated global dataset of coral bleaching observations (n=35,769) from 1985 to 2017 and satellite‐derived datasets of SST and clouds to examine for the first time at a global scale the influence of cloudiness on the likelihood of bleaching from thermal stress. We find that among coral reefs exposed to severe bleaching‐level heat stress (Degree Heating Weeks > 8°Cˑweek), bleaching severity is inversely correlated with the interaction of heat stress and cloud fraction anomalies (p<0.05), such that higher cloudiness implies reduced bleaching response. A Random Forest model analysis employing different set of environmental variables shows that a model employing Degree Heating Weeks and the 30‐day cloud fraction anomaly most accurately predicts bleaching severity (Accuracy = 0.834; Cohen’s Kappa = 0.769). Based on these results and global warm‐season cloudiness patterns, we develop a ‘cloudy refugia’ index which identifies the central equatorial Pacific and French Polynesia as regions where cloudiness is most likely to protect corals from bleaching. Our findings suggest that incorporating cloudiness into prediction models can help delineate bleaching responses and identify reefs which may be more resilient to climate change.