Polynesia was settled in a series of extraordinary voyages across an ocean spanning one third of the Earth , but the sequences of islands settled remain unknown and their timings disputed. Currently, several centuries separate the dates suggested by different archaeological surveys . Here, using genome-wide data from merely 430 modern individuals from 21 key Pacific island populations and novel ancestry-specific computational analyses, we unravel the detailed genetic history of this vast, dispersed island network. Our reconstruction of the branching Polynesian migration sequence reveals a serial founder expansion, characterized by directional loss of variants, that originated in Samoa and spread first through the Cook Islands (Rarotonga), then to the Society (Tōtaiete mā) Islands (11th century), the western Austral (Tuha'a Pae) Islands and Tuāmotu Archipelago (12th century), and finally to the widely separated, but genetically connected, megalithic statue-building cultures of the Marquesas (Te Henua 'Enana) Islands in the north, Raivavae in the south, and Easter Island (Rapa Nui), the easternmost of the Polynesian islands, settled in approximately AD 1200 via Mangareva.