Recent genomic analyses have provided substantial evidence for past periods of gene flow from polar bears (Ursus maritimus) into Alaskan brown bears (Ursus arctos), with some analyses suggesting a link between climate change and genomic introgression. However, because it has mainly been possible to sample bears from the present day, the timing, frequency, and evolutionary significance of this admixture remains unknown. Here, we analyze genomic DNA from three additional and geographically distinct brown bear populations, including two that lived temporally close to the peak of the last ice age. We find evidence of admixture in all three populations, suggesting that admixture between these species has been common in their recent evolutionary history. In addition, analyses of ten fossil bears from the now-extinct Irish population indicate that admixture peaked during the last ice age, whereas brown bear and polar bear ranges overlapped. Following this peak, the proportion of polar bear ancestry in Irish brown bears declined rapidly until their extinction. Our results support a model in which ice age climate change created geographically widespread conditions conducive to admixture between polar bears and brown bears, as is again occurring today. We postulate that this model will be informative for many admixing species pairs impacted by climate change. Our results highlight the power of paleogenomics to reveal patterns of evolutionary change that are otherwise masked in contemporary data.