Copy number variants (CNVs) are subject to stronger selective pressure than single-nucleotide variants, but their roles in archaic introgression and adaptation have not been systematically investigated. We show that stratified CNVs are significantly associated with signatures of positive selection in Melanesians and provide evidence for adaptive introgression of large CNVs at chromosomes 16p11.2 and 8p21.3 from Denisovans and Neanderthals, respectively. Using long-read sequence data, we reconstruct the structure and complex evolutionary history of these polymorphisms and show that both encode positively selected genes absent from most human populations. Our results collectively suggest that large CNVs originating in archaic hominins and introgressed into modern humans have played an important role in local population adaptation and represent an insufficiently studied source of large-scale genetic variation.