As Earth's climate has varied strongly through geological time, studying the impacts of past climate change on biodiversity helps to understand the risks from future climate change. However, it remains unclear how paleoclimate shapes spatial variation in biodiversity. Here, we assessed the influence of Quaternary climate change on spatial dissimilarity in taxonomic, phylogenetic, and functional composition among neighboring 200-kilometer cells (beta-diversity) for angiosperm trees worldwide. We found that larger glacial-interglacial temperature change was strongly associated with lower spatial turnover (species replacements) and higher nestedness (richness changes) components of beta-diversity across all three biodiversity facets. Moreover, phylogenetic and functional turnover was lower and nestedness higher than random expectations based on taxonomic beta-diversity in regions that experienced large temperature change, reflecting phylogenetically and functionally selective processes in species replacement, extinction, and colonization during glacial-interglacial oscillations. Our results suggest that future human-driven climate change could cause local homogenization and reduction in taxonomic, phylogenetic, and functional diversity of angiosperm trees worldwide.