Invasive species represent one of the foremost risks to global biodiversity. Here, we use population genomics to evaluate the history and consequences of an invasion of wild tomato—Solanum pimpinellifolium—onto the Galápagos islands from continental South America. Using >300 archipelago and mainland collections, we infer this invasion was recent and largely the result of a single event from central Ecuador. Patterns of ancestry within the genomes of invasive plants also reveal post-colonization hybridization and introgression between S. pimpinellifolium and the closely related Galapagos endemic Solanum cheesmaniae. Of admixed invasive individuals, those that carry endemic alleles at one of two different carotenoid biosynthesis loci also have orange fruits— characteristic of the endemic species—instead of typical red S. pimpinellifolium fruits. We infer that introgression of two independent fruit color loci explains this observed trait convergence, suggesting that selection has favored repeated transitions of red to orange fruits on the Galapagos.