The Cycladic, the Minoan, and the Helladic (Mycenaean) cultures define the Bronze Age (BA) of Greece. Urbanism, complex social structures, craft and agricultural specialization, and the earliest forms of writing characterize this iconic period. We sequenced six Early to Middle BA whole genomes, along with 11 mitochondrial genomes, sampled from the three BA cultures of the Aegean Sea. The Early BA (EBA) genomes are homogeneous and derive most of their ancestry from Neolithic Aegeans, contrary to earlier hypotheses that the Neolithic- EBA cultural transition was due to massive population turnover. EBA Aegeans were shaped by relatively small-scale migration from East of the Aegean, as evidenced by the Caucasus-related ancestry also detected in Anatolians. In contrast, Middle BA (MBA) individuals of northern Greece differ from EBA populations in showing similar to 50% Pontic-Caspian Steppe-related ancestry, dated at ca. 2,600-2,000 BCE. Such gene flow events during the MBA contributed toward shaping present-day Greek genomes.