The control and eradication of invasive species is a common management strategy to protect or restore native biodiversity. On South Georgia in the Southern Ocean, the brown rat Rattus norvegicus was brought onto the island with the onset of whaling and sealing activity in the 1800s and has had a significant detrimental impact on key bird species of conservation concern. Efforts to eradicate rats from South Georgia using poisoned bait are ongoing. Despite the South Georgia rat eradication programme being the geographically largest and most ambitious eradication initiative to date, its success is facilitated by the potential that rat populations are effectively isolated by glacial barriers. This allows for localized eradication effort at manageable scales, leading to sequential eradication of individual populations with minimal risk of incursion from neighbouring areas. Here, we use the levels of population genetic divergence estimated from 299 single nucleotide polymorphism (SNP) loci and DNA sequence variation across 993 base pairs of the mitochondrial DNA cytochrome B locus to examine whether rat populations from nine glacially isolated areas on South Georgia are genetically distinct and so can be treated as independent eradication units. Bayesian clustering of individuals based on SNP similarity identified seven different genetic groups, which were confirmed using analyses based on pairwise genetic distance estimates and ordination of individuals using principal coordinate analysis. From a management perspective, these seven groups represent individual targets in baiting operations. Two mtDNA haplotypes were resolved across South Georgia, with a distinct geographical separation between the north-western and south-eastern populations. Approximate Bayesian computation (ABC) was used to identify that this divergence was a consequence of two separate historical colonization events. Synthesis and applications. We illustrate that molecular markers are a valuable tool in species management and pest eradication given that the spatial distribution of genetic diversity can: (i) identify demographically and genetically independent populations on which local eradication effort can be focussed, (ii) distinguish between incomplete eradication and immigration in situations where individuals remain after eradication has been attempted and (iii) identify the source of migrants when dispersal occurs over large spatial scales.