Genetic studies of human evolution require high-quality contiguous ape genome assemblies that are not guided by the human reference. We coupled long-read sequence assembly and full-length complementary DNA sequencing with a multiplatform scaffolding approach to produce ab initio chimpanzee and orangutan genome assemblies. By comparing these with two long-read de novo human genome assemblies and a gorilla genome assembly, we characterized lineage-specific and shared great ape genetic variation ranging from single- to mega-base pair-sized variants. We identified ~17,000 fixed human-specific structural variants identifying genic and putative regulatory changes that have emerged in humans since divergence from nonhuman apes. Interestingly, these variants are enriched near genes that are down-regulated in human compared to chimpanzee cerebral organoids, particularly in cells analogous to radial glial neural progenitors.