The potential compounding behaviour of heatwaves and extreme rainfall have important implications for a range of hazards, including wildfires and flooding, yet remain poorly understood. In this global study, we analyse the likelihood of extreme 1-hr rainfall immediately following a heatwave, and identify climate zones where this phenomenon is most pronounced. We find the strongest compounding heatwave-extreme rainfall relationships in central Europe and Japan, where the likelihood of extreme rainfall after a heatwave is increased by approximately four times compared to climatology. Significant compounding is found mainly in temperate or colder climates, provided these areas receive ample moisture. As both heatwaves and extreme rainfall are expected to become more frequent in the future, our results indicate that the potential impacts from compounding heatwave-extreme rainfall events might significantly increase as well.