The history of human populations in the islands of the central and western Mediterranean is poorly understood. Here, the authors generate ancient-DNA data from the Balearic Islands, Sicily and Sardinia, and estimate the level and timing of steppe pastoralist, Iranian and North African ancestries in these populations. Steppe-pastoralist-related ancestry reached Central Europe by at least 2500 bc, whereas Iranian farmer-related ancestry was present in Aegean Europe by at least 1900 bc. However, the spread of these ancestries into the western Mediterranean, where they have contributed to many populations that live today, remains poorly understood. Here, we generated genome-wide ancient-DNA data from the Balearic Islands, Sicily and Sardinia, increasing the number of individuals with reported data from 5 to 66. The oldest individual from the Balearic Islands (2400 bc) carried ancestry from steppe pastoralists that probably derived from west-to-east migration from Iberia, although two later Balearic individuals had less ancestry from steppe pastoralists. In Sicily, steppe pastoralist ancestry arrived by 2200 bc, in part from Iberia; Iranian-related ancestry arrived by the mid-second millennium bc, contemporary to its previously documented spread to the Aegean; and there was large-scale population replacement after the Bronze Age. In Sardinia, nearly all ancestry derived from the island's early farmers until the first millennium bc, with the exception of an outlier from the third millennium bc, who had primarily North African ancestry and who-along with an approximately contemporary Iberian-documents widespread Africa-to-Europe gene flow in the Chalcolithic. Major immigration into Sardinia began in the first millennium bc and, at present, no more than 56-62% of Sardinian ancestry is from its first farmers. This value is lower than previous estimates, highlighting that Sardinia, similar to every other region in Europe, has been a stage for major movement and mixtures of people.