How individual animals respond to climate change is key to whether populations will persist or go extinct. Yet, few studies investigate how changes in individual behavior underpin these population-level phenomena. Shifts in the distributions of migratory animals can occur through adaptation in migratory behaviors, but there is little understanding of how selection and plasticity contribute to population range shift. Here, we use long-term geolocator tracking of Balearic shearwaters (Puffinus mauretanicus) to investigate how year-to-year changes in individual birds' migrations underpin a range shift in the post-breeding migration. We demonstrate a northward shift in the post-breeding range and show that this is brought about by individual plasticity in migratory destination, with individuals migrating further north in response to changes in sea-surface temperature. Furthermore, we find that when individuals migrate further, they return faster, perhaps minimizing delays in return to the breeding area. Birds apparently judge the increased distance that they will need to migrate via memory of the migration route, suggesting that spatial cognitive mechanisms may contribute to this plasticity and the resulting range shift. Our study exemplifies the role that individual behavior plays in populations' responses to environmental change and highlights some of the behavioral mechanisms that might be key to understanding and predicting species persistence in response to climate change.