Populations genetically related to present-day Europeans first appeared in Europe at some point after 38-40,000 years ago, following a cold period of severe climatic disruption. These new migrants would eventually replace the pre-existing modern human ancestries in Europe, but initial interactions between these groups are unclear due to the lack of genomic evidence from the earliest periods of the migration. Here we describe the genomes of two 36-37,000-year-old individuals from Buran-Kaya III in Crimea as belonging to this newer migration. Both genomes share the highest similarity to Gravettian-associated individuals found several thousand years later in southwestern Europe. These genomes also revealed that the population turnover in Europe after 40,000 years ago was accompanied by admixture with pre-existing modern human populations. European ancestry prior to 40,000 years ago persisted not only at Buran-Kaya III, but is also found in later Gravettian-associated populations of western Europe and Mesolithic Caucasus populations.