Theory predicts that when populations are established by few individuals, random founder effects can facilitate rapid phenotypic divergence even in the absence of selective processes. However, empirical evidence from historically documented colonisations suggest that, in most cases, drift alone is not sufficient to explain the rate of morphological divergence. Here, using the human-mediated introduction of the silvereye (Zosterops lateralis) to French Polynesia, which represents a potentially extreme example of population founding, we reassess the potential for morphological shifts to arise via drift alone. Despite only 80 years of separation from their New Zealand ancestors, French Polynesian silvereyes displayed significant changes in body and bill size and shape, most of which could be accounted for by drift, without the need to invoke selection. However, signatures of selection at genes previously identified as candidates for bill size and body shape differences in a range of bird species, also suggests a role for selective processes in driving morphological shifts within this population. Twenty-four SNPs in our RAD-Seq dataset were also found to be strongly associated with phenotypic variation. Hence, even under population founding extremes, when it is difficult to reject drift as the sole mechanism based on rate tests of phenotypic shifts, the additional role of divergent natural selection in novel environments can be revealed at the level of the genome.