•Premise of the Study:Climate change forces many species to migrate. Empirical small‐scale data on migration and colonization in the Arctic are scarce. Retreating glaciers provide new territory for cold‐adapted plant species, but the genetic consequences depend on dispersal distances and frequencies. We estimated local, regional, and long‐distance dispersal frequencies, as well as their effect on levels of genetic diversity, in diploid and tetraploid individuals ofSaxifraga oppositifolia.•Methods:Samples were collected in four aged moraines in each of three glacier forelands, in surrounding areas and reference populations in the Arctic archipelago Svalbard. These samples were analyzed for neutral amplified fragment length polymorphisms (AFLPs,n= 707) and ploidy levels (n= 30).•Key Results:Genetic clustering and ploidy analyses revealed two distinct genetic groups representing diploids and tetraploids, with few intermediate triploids. The groups were intermixed in most sampled populations. No differences in genetic diversity were found between tetraploids and diploids, or between established and glacier foreland populations. Seeds were dispersed over local, regional, and long distances, with the highest proportions of seeds originating from close sources. A minimum of 4–15 founding individuals from several source populations had initially established in each glacier foreland.•Conclusions:Our data suggest thatS. oppositifoliacan rapidly colonize new deglaciated areas without losing genetic diversity. Thus, glacier forelands can be alternative habitats for cold‐adapted vascular plants tracking their climatic niche. Our data show no difference in colonization success between diploid and tetraploid individuals.