The human genome contains many remnants of its evolutionary history, including a large number of evolutionarily volatile loci which have been introduced since our divergence from primates. One particularly intriguing source of novel DNA sequences is introgression events with archaic species which co-existed with modern humans. Both Neanderthals, who were common in Europe, and Denisovans, who have been observed only in Asia, have contributed genetic variants to the modern human genome but the functional consequences of these introgressed variants have yet to be investigated systematically. In this work, we show that Neanderthal and Denisovan DNA is most enriched for genetic variants which regulate gene expression in Europe and East Asia respectively, i.e. the populations in which the introgression event(s) most contributed to contemporary genetic variation. Neanderthal eQTLs, in particular, frequently upregulate gene expression. Archaic eQTLs from these two species regulate target genes with similar molecular functions which are distinct in each contemporary population, with the only common enrichment being for Neanderthal eQTLs to regulate taste receptor genes in both Europe and East Asia. We observed a correlated pattern of enrichment and depletion of medical phenotypes across Neanderthal and Denisovan eQTLs, including a shared enrichment for CNVs associated with developmental delay. Our results demonstrate the role of functional archaic DNA in regulating molecular phenotypes and disease risk across global populations and confirm the relevance of recently acquired DNA to contemporary human genetic variation.