Sexual selection is proposed to be a powerful driver of phenotypic evolution in animal systems. At macroevolutionary scales, sexual selection can theoretically drive both the rate and direction of phenotypic evolution, but this hypothesis remains contentious. Here, we find that differences in the rate and direction of plumage colour evolution are predicted by a proxy for sexual selection intensity (plumage dichromatism) in a large radiation of suboscine passerine birds (Tyrannida). We show that rates of plumage evolution are correlated between the sexes, but that sexual selection has a strong positive effect on male, but not female, interspecific divergence rates. Furthermore, we demonstrate that rapid male plumage divergence is biased towards carotenoid-based (red/yellow) colours widely assumed to represent honest sexual signals. Our results highlight the central role of sexual selection in driving avian colour divergence, and reveal the existence of convergent evolutionary responses of animal signalling traits under sexual selection.