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Huns, Avars, and conquering Hungarians were migration-period nomadic tribal confederations that arrived in three successive waves in the Carpathian Basin between the 5th and 9th centuries. Based on the historical data, each of these groups are thought to have arrived from Asia, although their exact origin and relation to other ancient and modern populations have been debated. Recently, hundreds of ancient genomes were analyzed from Central Asia, Mongolia, and China, from which we aimed to identify putative source populations for the above-mentioned groups. In this study, we have sequenced 9 Hun, 143 Avar, and 113 Hungarian conquest period samples and identified three core populations, representing immigrants from each period with no recent European ancestry. Our results reveal that this "immigrant core" of both Huns and Avars likely originated in present day Mongolia, and their origin can be traced back to Xiongnus (Asian Huns), as suggested by several historians. On the other hand, the "immigrant core" of the conquering Hungarians derived from an earlier admixture of Mansis, early Sarmatians, and descendants of late Xiongnus. We have also shown that a common "proto-Ugric" gene pool appeared in the Bronze Age from the admixture of Mezhovskaya and Nganasan people, supporting genetic and linguistic data. In addition, we detected shared Hun-related ancestry in numerous Avar and Hungarian conquest period genetic outliers, indicating a genetic link between these successive nomadic groups. Aside from the immigrant core groups, we identified that the majority of the individuals from each period were local residents harboring "native European" ancestry. • 265 new ancient genomes help to unravel the origin of migration-period populations • Genetic continuity is detected between Xiongnus and European Huns • European Avars most likely originated from Mongolia and were related to Huns • Conquering Hungarians had Ugric ancestry and later admixed with Sarmatians and Huns Maróti et al. show that immigrants were in minority compared with the locals of the Carpathian Basin in each period. Several Hun period immigrants had Asian Hun (Xiongnu) ancestry. The Avar immigrant elite had ancient Mongolian origin. Conquering Hungarians and Mansis had common ancestors, but proto-Hungarians further admixed with Sarmatians and Huns. [ABSTRACT FROM AUTHOR]