Nutria (Myocastor coypus) are semi‐aquatic rodents native to South America, introduced to the USA for fur farming during the early twentieth century. This species' herbivory can cause extensive damage to agriculture and wetland ecosystems. Although declared eradicated from California, USA, in the 1970s, nutria populations were recently discovered in the state's Central Valley and subsequently in the Sacramento–San Joaquin Delta, areas of significant agricultural and conservation importance. We report the use of a combination of nuclear single-nucleotide polymorphisms (SNPs) and mitochondrial (mtDNA; cytochrome b locus) markers to characterize the source and demographic history of the current invasion, to inform eradication efforts. Our study is the first to develop a SNP dataset for nutria, utilizing 6809 loci to characterize genetic diversity in comparison to several potential source populations. Multivariate analysis and Bayesian clustering of the SNP dataset found the greatest similarity to invasive nutria in central Oregon, USA, with minimal genetic differentiation in the Central Valley, excluding the leading edges of the invasion. Cytochrome b sequencing yielded a single contemporary California haplotype shared with nutria in Oregon and Washington, as well as in museum samples from California fur farms that predated eradication. Mantel tests found genetic differentiation between nutria in the Central Valley was best explained by ecological distance along rivers, while estimated effective migration surface (EEMS) analysis indicated gene flow was characterized by infrequent dispersal followed by rapid expansion in large, protected areas of emergent wetland habitat. These combined findings suggest contemporary California nutria represent a recent introduction that underwent rapid expansion. Our data further support treating the Central Valley as a single eradication unit while investing additional resources in targeting dispersal corridors to best achieve management goals. This study presents the first characterization of a regional nutria invasion within the larger context of global population and phylogenetics.