The debate concerning the origin of the Polynesian speaking peoples has been recently reinvigorated by genetic evidence for secondary migrations to western Polynesia from the New Guinea region during the 2nd millennium BP. Using genome-wide autosomal data from the Leeward Society Islands, the ancient cultural hub of eastern Polynesia, we find that the inhabitants' genomes also demonstrate evidence of this episode of admixture, dating to 1,700-1,200 BP. This supports a late settlement chronology for eastern Polynesia, commencing ~1,000 BP, after the internal differentiation of Polynesian society. More than 70% of the autosomal ancestry of Leeward Society Islanders derives from Island Southeast Asia with the lowland populations of the Philippines as the single largest potential source. These long-distance migrants into Polynesia experienced additional admixture with northern Melanesians prior to the secondary migrations of the 2nd millennium BP. Moreover, the genetic diversity of mtDNA and Y chromosome lineages in the Leeward Society Islands is consistent with linguistic evidence for settlement of eastern Polynesia proceeding from the central northern Polynesian outliers in the Solomon Islands. These results stress the complex demographic history of the Leeward Society Islands and challenge phylogenetic models of cultural evolution predicated on eastern Polynesia being settled from Samoa.