A better understanding of the genetic and ecological factors underlying successful invasions is critical to mitigate the negative impacts of invasive species. Here, we study the invasion history of Helianthus annuus populations from Argentina, with particular emphasis on the role of post‐introduction admixture with cultivated sunflower (also H. annuus) and climate adaptation driven by large haploblocks. We conducted genotyping‐by‐sequencing of samples of wild populations as well as Argentinian cultivars and compared them with wild (including related annual Helianthus species) and cultivated samples from the native range. We also characterised samples for 11 known haploblocks associated with environmental variation in native populations to test whether haploblocks contributed to invasion success. Population genomics analyses supported two independent geographic sources for Argentinian populations, the central United States and Texas, but no significant contribution of related annual Helianthus species. We found pervasive admixture with cultivated sunflower, likely as result of post‐introduction hybridization. Genomic scans between invasive populations and their native sources identified multiple genomic regions of divergence, possibly indicative of selection, in the invaded range. These regions significantly overlapped between the two native‐invasive comparisons and showed disproportionally high crop ancestry, suggesting that crop alleles contributed to invasion success. We did not find evidence of climate adaptation mediated by haploblocks, yet outliers of genome scans were enriched in haploblock regions and, for at least two haploblocks, the cultivar haplotype was favoured in Argentina. Our results show that admixture with cultivated sunflower played a major role in the establishment and spread of H. annuus populations in Argentina.