The complete assembly of each human chromosome is essential for understanding human biology and evolution^1,2. Here we use complementary long-read sequencing technologies to complete the linear assembly of human chromosome 8. Our assembly resolves the sequence of five previously long-standing gaps, including a 2.08-Mb centromeric α-satellite array, a 644-kb copy number polymorphism in the β-defensin gene cluster that is important for disease risk, and an 863-kb variable number tandem repeat at chromosome 8q21.2 that can function as a neocentromere. We show that the centromeric α-satellite array is generally methylated except for a 73-kb hypomethylated region of diverse higher-order α-satellites enriched with CENP-A nucleosomes, consistent with the location of the kinetochore. In addition, we confirm the overall organization and methylation pattern of the centromere in a diploid human genome. Using a dual long-read sequencing approach, we complete high-quality draft assemblies of the orthologous centromere from chromosome 8 in chimpanzee, orangutan and macaque to reconstruct its evolutionary history. Comparative and phylogenetic analyses show that the higher-order α-satellite structure evolved in the great ape ancestor with a layered symmetry, in which more ancient higher-order repeats locate peripherally to monomeric α-satellites. We estimate that the mutation rate of centromeric satellite DNA is accelerated by more than 2.2-fold compared to the unique portions of the genome, and this acceleration extends into the flanking sequence.