The maritime expansion of Scandinavian populations during the Viking Age (about AD 750-1050) was a far-flung transformation in world history^1,2. Here we sequenced the genomes of 442 humans from archaeological sites across Europe and Greenland (to a median depth of about 1×) to understand the global influence of this expansion. We find the Viking period involved gene flow into Scandinavia from the south and east. We observe genetic structure within Scandinavia, with diversity hotspots in the south and restricted gene flow within Scandinavia. We find evidence for a major influx of Danish ancestry into England; a Swedish influx into the Baltic; and Norwegian influx into Ireland, Iceland and Greenland. Additionally, we see substantial ancestry from elsewhere in Europe entering Scandinavia during the Viking Age. Our ancient DNA analysis also revealed that a Viking expedition included close family members. By comparing with modern populations, we find that pigmentation-associated loci have undergone strong population differentiation during the past millennium, and trace positively selected loci-including the lactase-persistence allele of LCT and alleles of ANKA that are associated with the immune response-in detail. We conclude that the Viking diaspora was characterized by substantial transregional engagement: distinct populations influenced the genomic makeup of different regions of Europe, and Scandinavia experienced increased contact with the rest of the continent.