Elucidating processes and mechanisms involved in rapid local adaptation to varied environments is a poorly understood but crucial component in management of invasive species. Recent studies have proposed that genetic and epigenetic variation could both contribute to ecological adaptation, yet it remains unclear on the interplay between these two components underpinning rapid adaptation in wild animal populations. To assess their respective contributions to local adaptation, we explored epigenomic and genomic responses to environmental heterogeneity in eight recently colonized ascidian (Ciona intestinalis) populations at a relatively fine geographical scale. Based on MethylRADseq data, we detected strong patterns of local environment-driven DNA methylation divergence among populations, significant epigenetic isolation by environment (IBE), and a large number of local environment-associated epigenetic loci. Meanwhile, multiple genetic analyses based on single nucleotide polymorphisms (SNPs) showed genomic footprints of divergent selection. In addition, for five genetically similar populations, we detected significant methylation divergence and local environment-driven methylation patterns, indicating the strong effects of local environments on epigenetic variation. From a functional perspective, a majority of functional genes, Gene Ontology (GO) terms, and biological pathways were largely specific to one of these two types of variation, suggesting partial independence between epigenetic and genetic adaptation. The methylation quantitative trait loci (mQTL) analysis showed that the genetic variation explained only 18.67% of methylation variation, further confirming the autonomous relationship between these two types of variation. Altogether, we highlight the complementary interplay of genetic and epigenetic variation involved in local adaptation, which may jointly promote populations' rapid adaptive capacity and successful invasions in different environments. The findings here provide valuable insights into interactions between invaders and local environments to allow invasive species to rapidly spread, thus contributing to better prediction of invasion success and development of management strategies.