The majority of human chromosome ends remain incomplete due to their highly repetitive structure. In this study, we use BioNano data to anchor and extend chromosome ends from two European trios as well as two unrelated Asian genomes. Two thirds of BioNano assembled chromosome ends are structurally divergent from the reference genome, including both deletions and extensions. The majority of extensions are homologous to sequences on chromosome 1p, 5q and 19p. These extensions are heritable and in some cases divergent between Asian and European samples. We identified two sequence families in these sequences which have undergone substantial duplication in multiple primate lineages, leading to the formation of new fusion genes. We show that these sequence families have arisen from progenitor interstitial sequence on the ancestral primate chromosome 7. Comparison of chromosome end sequences from 15 species revealed that chromosome end divergence matches the corresponding phylogenetic relationship and revealed a rate of chromosome extension since the primate divergence of 80-440 kbp per million years.