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The role of selection in shaping genetic diversity in natural populations is an area of intense interest in modern biology, especially the characterization of adaptive loci. Within humans, the rapid increase in genomic information has produced surprisingly few well-defined adaptive loci, promoting the view that recent human adaptation involved numerous loci with small fitness benefits. To examine this we searched for signatures of hard sweeps – the selective fixation of a new or initially rare beneficial variant – in 1,162 ancient western Eurasian genomes and identified 57 sweeps with high confidence. This unexpectedly extensive signal was concentrated on proteins acting at the cell surface, and potential selection pressures include cold adaptation in early Eurasian populations, and oxidative stress from carbohydrate-rich diets in farming populations. Critically, these sweep signals have been obscured in modern European genomes by subsequent population admixture, especially during the Bronze Age (5-3kya) and empires of classical antiquity.