Invasive species cause considerable ecological and economic damage. Despite decades of broad impacts of invasives on diversity and agriculture, the genetic adaptations and near-term evolution of invading populations are poorly understood. The fall webworm, Hyphantria cunea, a highly successful invasive species that originated in North America, spread throughout the Northern Hemisphere during the past 80 years. Here, we use whole-genome sequencing of invasive populations and transcriptome profiling to probe the underlying genetic bases for the rapid adaptation of this species to new environments and host plants. We find substantial reductions in genomic diversity consistent with founder effects. Genes and pathways associated with carbohydrate metabolism and gustatory receptors are substantially expanded in the webworm genome and show strong signatures of functional polymorphisms in the invasive population. We also find that silk-yielding-associated genes maintained a relatively low level of functional diversity, and identify candidate genes that may regulate the development of silk glands in fall webworms. These data suggest that the fall webworm's ability to colonize novel hosts, mediated by plasticity in their gustatory capabilities along with an increased ability to utilize novel nutrition sources and substrates, has facilitated the rapid and successful adaptation of the species throughout its range.