Human-mediated introductions have enabled species to colonize beyond their native ranges, yet the mechanisms underlying successful establishment remain unclear. We combined genomic and ecological analyses to investigate parallel introductions of the Eurasian Tree Sparrow across continents. Our analyses of genetic structure and demography revealed that introduced populations in North America (European origin) and Australia (Chinese origin) experienced founder effects, with resulting bottlenecks, reduced genetic diversity, and increased inbreeding. Despite the genome-wide loss of diversity, we identified conserved regions of high genetic variation in the introduced populations, potentially maintained through balancing selection of ancestral polymorphisms. Genotype-climate association and genetic offset modeling demonstrated that climate-adaptive genetic variants retained similar frequencies across the native and introduced ranges, likely maintaining similar interactions of genetic components with climate niches. Our findings highlight how retention of adaptive polymorphism facilitates establishment success in the introduced populations, providing a framework for predicting invasion potential through genomic signatures of adaptation.