The Neolithic and Bronze Age transitions were profound cultural shifts catalyzed in parts of Europe by migrations, first of early farmers from the Near East and then Bronze Age herders from the Pontic Steppe. However, a decades-long, unresolved controversy is whether population change or cultural adoption occurred at the Atlantic edge, within the British Isles. We address this issue by using the first whole genome data from prehistoric Irish individuals. A Neolithic woman (3343-3020 cal BC) from a megalithic burial (10.3× coverage) possessed a genome of predominantly Near Eastern origin. She had some hunter-gatherer ancestry but belonged to a population of large effective size, suggesting a substantial influx of early farmers to the island. Three Bronze Age individuals from Rathlin Island (2026-1534 cal BC), including one high coverage (10.5×) genome, showed substantial Steppe genetic heritage indicating that the European population upheavals of the third millennium manifested all of the way from southern Siberia to the western ocean. This turnover invites the possibility of accompanying introduction of Indo-European, perhaps early Celtic, language. Irish Bronze Age haplotypic similarity is strongest within modern Irish, Scottish, and Welsh populations, and several important genetic variants that today show maximal or very high frequencies in Ireland appear at this horizon. These include those coding for lactase persistence, blue eye color, Y chromosome R1b haplotypes, and the hemochromatosis C282Y allele; to our knowledge, the first detection of a known Mendelian disease variant in prehistory. These findings together suggest the establishment of central attributes of the Irish genome 4,000 y ago.