Ancient DNA analysis of three individuals dated to ~3000 years before present (BP) from Vanuatu and one ~2600 BP individual from Tonga has revealed that the first inhabitants of Remote Oceania ("First Remote Oceanians") were almost entirely of East Asian ancestry, and thus their ancestors passed New Guinea, the Bismarck Archipelago, and the Solomon Islands with minimal admixture with the Papuan groups they encountered [1]. However, all present-day populations in Near and Remote Oceania harbor 25-100% Papuan ancestry, implying that there must have been at least one later stream of migration eastward from Near Oceania. We generated genome-wide data for 14 ancient individuals from Efate and Epi Islands in Vanuatu ranging from 3,000-150 BP, along with 185 present-day Vanuatu individuals from 18 islands. We show that people of almost entirely Papuan ancestry had arrived in Vanuatu by 2400 BP, an event that coincided with the end of the Lapita cultural period, changes in skeletal morphology, and the cessation of long-distance trade between Near and Remote Oceania [2]. First Remote Oceanian ancestry subsequently increased via admixture but remains at 10-20% in most islands. Through a fine-grained comparison of ancestry profiles in Vanuatu and Polynesia with diverse groups in Near Oceania, we find that Papuan ancestry in Vanuatu is consistent with deriving from the Bismarck Archipelago instead of the geographically closer Solomon Islands. Papuan ancestry in Polynesia also shows connections to the ancestry profiles present in the Bismarck Archipelago but is more similar to Tolai from New Britain and Tutuba from Vanuatu than to the ancient Vanuatu individuals and the great majority of present-day Vanuatu populations. This suggests a third eastward stream of migration from Near to Remote Oceania bringing a different type of Papuan ancestry