One of the most long-standing and important mysteries in evolutionary biology is why biological diversity is so unevenly distributed across space and taxonomic lineages. Nowhere is this disparity more evident than in the multitude of rapid evolutionary radiations found on oceanic islands and mountain ranges across the globe [1-5]. The evolutionary processes driving these rapid diversification events remain unclear [6-8]. Recent genome-wide studies suggest that natural selection may be frequent during rapid evolutionary radiations, as inferred from work in cichlid fish [9], white-eye birds [10], new world lupins [11], and wild tomatoes [12]. However, whether frequent adaptive evolution is a general feature of rapid evolutionary radiations remains untested. Here we show that adaptive evolution is significantly more frequent in rapid evolutionary radiations compared to background levels in more slowly diversifying lineages. This result is consistent across a wide range of angiosperm lineages analyzed: 12 evolutionary radiations, which together comprise 1,377 described species, originating from some of the most biologically diverse systems on Earth. In addition, we find a significant negative correlation between population size and frequency of adaptive evolution in rapid evolutionary radiations. A possible explanation for this pattern is that more frequent adaptive evolution is at least partly driven by positive selection for advantageous mutations that compensate for the fixation of slightly deleterious mutations in smaller populations.