Human accelerated regions (HARs) are conserved genomic loci that evolved at an accelerated rate in the human lineage and may underlie human-specific traits. We generated HARs and chimpanzee accelerated regions with an automated pipeline and an alignment of 241 mammalian genomes. Combining deep learning with chromatin capture experiments in human and chimpanzee neural progenitor cells, we discovered a significant enrichment of HARs in topologically associating domains containing human-specific genomic variants that change three-dimensional (3D) genome organization. Differential gene expression between humans and chimpanzees at these loci suggests rewiring of regulatory interactions between HARs and neurodevelopmental genes. Thus, comparative genomics together with models of 3D genome folding revealed enhancer hijacking as an explanation for the rapid evolution of HARs.