Poleward range expansions are commonly attributed to global change, but could alternatively be driven by rapid evolutionary adaptation. A well-documented example of a range expansion during the past decades is provided by the European wasp spider Argiope bruennichi. Using ecological niche modeling, thermal tolerance experiments and a genome-wide analysis of gene expression divergence, we show that invasive populations have adapted to novel climatic conditions in the course of their expansion. Their climatic niche shift is mirrored in an increased cold tolerance and a population-specific and functionally differentiated gene expression response. We generated an Argiope reference genome sequence and used population genome resequencing to assess genomic changes associated with the new climatic adaptations. We find clear genetic differentiation and a significant admixture with alleles from East Asian populations in the invasive Northern European populations. Population genetic modeling suggests that at least some of these introgressing alleles have contributed to the new adaptations during the expansion. Our results thus confirm the notion that range expansions are not a simple consequence of climate change, but are accompanied by fast genetic changes and adaptations that may be fuelled through admixture between long separated lineages.