Many species are shifting their ranges in response to climate‐driven environmental changes, particularly in high‐latitude regions. However, the patterns of dispersal and colonization during range shifting events are not always clear. Understanding how populations are connected through space and time can reveal how species navigate a changing environment. Here, we present a fine‐scale population genomics study of gentoo penguins (Pygoscelis papua), a presumed site‐faithful colonial nesting species that has increased in population size and expanded its range south along the Western Antarctic Peninsula. Using whole genome sequencing, we analysed 129 gentoo penguin individuals across 12 colonies located at or near the southern range edge. Through a detailed examination of fine‐scale population structure, admixture, and population divergence, we inferred that gentoo penguins historically dispersed rapidly in a stepping‐stone pattern from the South Shetland Islands leading to the colonization of Anvers Island, and then the adjacent mainland Western Antarctica Peninsula. Recent southward expansion along the Western Antarctic Peninsula also followed a stepping‐stone dispersal pattern coupled with limited post‐divergence gene flow from colonies on Anvers Island. Genetic diversity appeared to be maintained across colonies during the historical dispersal process, and range‐edge populations are still growing. This suggests large numbers of migrants may provide a buffer against founder effects at the beginning of colonization events to maintain genetic diversity similar to that of the source populations before migration ceases post‐divergence. These results coupled with a continued increase in effective population size since approximately 500–800 years ago distinguish gentoo penguins as a robust species that is highly adaptable and resilient to changing climate.