Robertsonian chromosomes are a type of variant chromosome found commonly in nature. Present in one in 800 humans, these chromosomes can underlie infertility, trisomies, and increased cancer incidence. Recognized cytogenetically for more than a century, their origins have remained mysterious. Recent advances in genomics allowed us to assemble three human Robertsonian chromosomes completely. We identify a common breakpoint and epigenetic changes in centromeres that provide insight into the formation and propagation of common Robertsonian translocations. Further investigation of the assembled genomes of chimpanzee and bonobo highlights the structural features of the human genome that uniquely enable the specific crossover event that creates these chromosomes. Resolving the structure and epigenetic features of human Robertsonian chromosomes at a molecular level paves the way to understanding how chromosomal structural variation occurs more generally, and how chromosomes evolve.