Summary Western Eurasia witnessed several large-scale human migrations during the Holocene 1–5 . To investigate the cross-continental impacts we shotgun-sequenced 317 primarily Mesolithic and Neolithic genomes from across Northern and Western Eurasia. These were imputed alongside published data to obtain diploid genotypes from >1,600 ancient humans. Our analyses revealed a ‘Great Divide’ genomic boundary extending from the Black Sea to the Baltic. Mesolithic hunter-gatherers (HGs) were highly genetically differentiated east and west of this zone, and the impact of the neolithisation was equally disparate. Large-scale ancestry shifts occurred in the west as farming was introduced, including near-total replacements of HGs in many areas, whereas no substantial ancestry shifts happened east of the zone during the same period. Similarly, relatedness decreased in the west from the Neolithic transition onwards, while east of the Urals relatedness remained high until ∼4,000 BP, consistent with persistence of localised HG groups. The boundary dissolved when Yamnaya-related ancestry spread across western Eurasia around 5,000 BP resulting in a second major turnover that reached most parts of Europe within a 1,000-year span. The genetic origin and fate of the Yamnaya have remained elusive but we demonstrate that HGs from the Middle Don region contributed ancestry to them. Yamnaya-groups later admixed with individuals associated with the Globular Amphora Culture before expanding into Europe. Similar turnovers occurred in western Siberia, where we report new genomic data from a ‘Neolithic steppe’ cline spanning the Siberian forest steppe to Lake Baikal. These prehistoric migrations had profound and lasting effects on the genetic diversity of Eurasian populations.