Advances in genomics have led to an appreciation that introgression is common, but its evolutionary consequences are poorly understood. In recent species radiations the sharing of genetic variation across porous species boundaries can facilitate adaptation to new environments and generate novel phenotypes, which may contribute to further diversification. Most Anopheles mosquito species that are of major importance as human malaria vectors have evolved within recent and rapid radiations of largely nonvector species. Here, we focus on one of the most medically important yet understudied anopheline radiations, the Afrotropical Anopheles funestus complex (AFC), to investigate the role of introgression in its diversification and the possible link between introgression and vector potential. The AFC comprises at least seven morphologically similar species, yet only An. funestus sensu stricto is a highly efficient malaria vector with a pan-African distribution. Based on de novo genome assemblies and additional whole-genome resequencing, we use phylogenomic and population genomic analyses to establish species relationships. We show that extensive interspecific gene flow involving multiple species pairs has shaped the evolutionary history of the AFC since its diversification. The most recent introgression event involved a massive and asymmetrical movement of genes from a distantly related AFC lineage into An. funestus, an event that predated and plausibly facilitated its subsequent dramatic geographic range expansion across most of tropical Africa. We propose that introgression may be a common mechanism facilitating adaptation to new environments and enhancing vectorial capacity in Anopheles mosquitoes.