Habitat ranges of most species shift over time, for instance due to climate change, human intervention, or adaptation. These demographic changes often have drastic population genetic effects, such as a stochastic resampling of the gene pool through the "surfing" phenomenon. Most models assume that the speed of range expansions is only limited by the dispersal ability of the colonizing species and its reproductive potential. While such models of "phenotype-limited" expansions apply to species invasions, it is clear that many range expansions are limited rather by the slow motion of habitat boundaries, as driven for instance by global warming. Here, we develop a coalescent model to study the genetic impact of such "boundary-limited" range expansions. Our simulations and analysis show that the resulting loss of genetic diversity is markedly lower than in species invasions if large carrying capacities can be maintained up to the habitat frontier. Counterintuitively, we find that the total loss of diversity does not depend on the speed of the range expansion: Slower expansions have a smaller rate of loss, but also last longer. Boundary-limited range expansions exhibit a characteristic genetic footprint and should therefore be distinguished from range expansions limited only by intrinsic characteristics of the species.