Recent genomic analyses show that the earliest peoples reaching Remote Oceania-associated with Austronesian-speaking Lapita culture-were almost completely East Asian, without detectable Papuan ancestry. However, Papuan-related genetic ancestry is found across present-day Pacific populations, indicating that peoples from Near Oceania have played a significant, but largely unknown, ancestral role. Here, new genome-wide data from 19 ancient South Pacific individuals provide direct evidence of a so-far undescribed Papuan expansion into Remote Oceania starting ~2,500 yr BP, far earlier than previously estimated and supporting a model from historical linguistics. New genome-wide data from 27 contemporary ni-Vanuatu demonstrate a subsequent and almost complete replacement of Lapita-Austronesian by Near Oceanian ancestry. Despite this massive demographic change, incoming Papuan languages did not replace Austronesian languages. Population replacement with language continuity is extremely rare-if not unprecedented-in human history. Our analyses show that rather than one large-scale event, the process was incremental and complex, with repeated migrations and sex-biased admixture with peoples from the Bismarck Archipelago.