Genomic instability is a hallmark of human cancers, including the 5% caused by human papillomavirus (HPV). Here we report a striking association between HPV integration and adjacent host genomic structural variation in human cancer cell lines and primary tumors. Whole-genome sequencing revealed HPV integrants flanking and bridging extensive host genomic amplifications and rearrangements, including deletions, inversions, and chromosomal translocations. We present a model of "looping" by which HPV integrant-mediated DNA replication and recombination may result in viral-host DNA concatemers, frequently disrupting genes involved in oncogenesis and amplifying HPV oncogenes E6 and E7. Our high-resolution results shed new light on a catastrophic process, distinct from chromothripsis and other mutational processes, by which HPV directly promotes genomic instability.