Geographic range shifts can cause secondary contact and hybridization between closely related species, revealing mechanisms of species formation and integrity. These dynamics typically play out in restricted geographic regions, but highly vagile species may experience major distributional changes resulting in broad areas of contact. The Glossy Ibis (Plegadis falcinellus) is a dispersive waterbird of the Old World and Australia that colonized eastern North America in the early 19th century and came into contact with the native White‐faced Ibis (P. chihi). Putative hybrids between the two species have been observed across North America. To examine the population genomic consequences of this natural invasion, we sequenced 4,616 ultraconserved elements from 66 individuals sampled across the distributions of falcinellus, chihi, and the Puna Ibis (P. ridgwayi) of South America. We found genomic differentiation among the three species. Loci with high sequence divergence were often shared across all pairwise species comparisons, were associated with regions of high nucleotide diversity, and were concentrated on the Z chromosome. We detected signals of genetic admixture between chihi and falcinellus in individuals both near and far from their core area of sympatry. Genomic cline analyses revealed evidence of greater introgression into falcinellus from chihi, but we found little evidence for selection against hybrids. We also found signals of admixture between ridgwayi and South American populations of chihi. Our results indicate vagile species can experience pervasive introgression upon secondary contact, although we suggest these dynamics may be more ephemeral than the stable hybrid zones often observed in less dispersive organisms.