Author summary Humans of Papuan ancestry owe roughly 5% of their genome to Denisovans, a poorly characterised archaic hominin. While introgressed DNA segments can be readily identified, understanding their biological consequences remains challenging. By examining the distribution of introgressed DNA against existing functional genomics datasets, it is possible to predict the phenotypes they impact. In Papuans, Denisovan DNA, but not Neanderthal, strongly and consistently affects immune cells and immune-related processes of potential evolutionary relevance. In vitro testing of introgressed variants confirms these predictions, suggesting Denisovan variants can impact gene regulation in vivo. Variation in gene expression might be key to understanding the consequences of admixture between modern humans and archaic hominins, as has been observed with Neanderthal DNA in other human populations.