We assembled genome-wide data from 271 ancient Iberians, of whom 176 are from the largely unsampled period after 2000 BCE, thereby providing a high-resolution time transect of the Iberian Peninsula. We document high genetic substructure between northwestern and southeastern hunter-gatherers before the spread of farming. We reveal sporadic contacts between Iberia and North Africa by ~2500 BCE and, by ~2000 BCE, the replacement of 40% of Iberia’s ancestry and nearly 100% of its Y-chromosomes by people with Steppe ancestry. We show that, in the Iron Age, Steppe ancestry had spread not only into Indo-European─speaking regions but also into non-Indo-European─speaking ones, and we reveal that present-day Basques are best described as a typical Iron Age population without the admixture events that later affected the rest of Iberia. Additionally, we document how, beginning at least in the Roman period, the ancestry of the peninsula was transformed by gene flow from North Africa and the eastern Mediterranean.