Experimental introductions of species have provided some of the most tractable examples of rapid phenotypic changes, which may reflect plasticity, the impact of stochastic processes, or the action of natural selection. Yet to date, very few studies have investigated the neutral and potentially adaptive genetic impacts of experimental introductions. We dissect the role of these processes in shaping the population differentiation of wall lizards in three Croatian islands (Sušac, Pod Kopište, and Pod Mrčaru), including the islet of Pod Mrčaru, where experimentally introduced lizards underwent rapid (~30 generations) phenotypic changes associated with a shift from an insectivorous to a plant‐based diet. Using a genomic approach (~82,000 ddRAD loci), we confirmed a founder effect during introduction and very low neutral genetic differentiation between the introduced population and its source. However, genetic depletion did not prevent rapid population growth, as the introduced lizards exhibited population genetic signals of expansion and are known to have reached a high density. Our genome‐scan analysis identified just a handful of loci showing large allelic shifts between ecologically divergent populations. This low overall signal of selection suggests that the extreme phenotypic differences observed among populations are determined by a small number of large‐effect loci and/or that phenotypic plasticity plays a major role in phenotypic changes. Nonetheless, functional annotation of the outlier loci revealed some candidate genes relevant to diet‐induced adaptation, in agreement with the hypothesis of directional selection. Our study provides important insights on the evolutionary potential of bottlenecked populations in response to new selective pressures on short ecological timescales.