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The genetic composition of founding populations is likely to play a key role in determining invasion success. Individual genotypes may differ in habitat preference and environmental tolerance, so their ability to colonize novel environments can be highly variable. Despite the importance of genetic variation on invasion success, its influence on the potential distribution of invaders is rarely investigated. Here, we integrate population genomics and ecological niche models (ENMs) into a single framework to predict the distribution of globally invasive common ragweed (Ambrosia artemisiifolia) in Australia. We identified three genetic clusters for ragweed and used these to construct cluster‐specific ENMs and characterize within‐species niche differentiation. The potential range of ragweed in Australia depended on the genetic composition and continent of origin of the introduced population. Invaders originating from warmer, wetter climates had a broader potential distribution than those from cooler, drier ones. By quantifying this change, we identified source populations most likely to expand the ragweed distribution. As prevention remains the most effective method of invasive species management, our work provides a valuable way of ranking the threat posed by different populations to better inform management decisions. [ABSTRACT FROM AUTHOR]