The introduction of non-native species into new habitats is one of the foremost risks to global biodiversity. Here, we evaluate a recent invasion of wild tomato (Solanum pimpinellifolium) onto the Galapagos islands from a population genomic perspective, using a large panel of novel collections from the archipelago as well as historical accessions from mainland Ecuador and Peru. We infer a recent invasion of S. pimpinellifolium on the islands, largely the result of a single event from central Ecuador which, despite its recency, has rapidly spread onto several islands in the Galapagos. By reconstructing patterns of local ancestry throughout the genomes of invasive plants, we uncover evidence for recent hybridization and introgression between S. pimpinellifolium and the closely related endemic species Solanum cheesmaniae. Two large introgressed regions overlap with known fruit color loci involved in carotenoid biosynthesis. Instead of red fruits, admixed individuals with endemic haplotypes at these loci have orange fruit colors that are typically characteristic of the endemic species. We therefore infer that introgression explains the observed trait convergence. Moreover, we infer roles for two independent loci in driving this pattern, and a likely history of selection favoring the repeated phenotypic transition fro m red to orange fruits. Together, our data reconstruct a complex history of invasion, expansion, and gene flow among wild tomatoes on the Galapagos islands. These findings provide critical data on the evolutionary importance of hybridization during colonization and its role in influencing conservation outcomes.