Most cancers are characterized by the somatic acquisition of genomic rearrangements during tumour evolution that eventually drive the oncogenesis. Here, using multiplatform sequencing technologies, we identify and characterize a remarkable mutational mechanism in human hepatocellular carcinoma caused by Hepatitis B virus, by which DNA molecules from the virus are inserted into the tumour genome causing dramatic changes in its configuration, including non-homologous chromosomal fusions, dicentric chromosomes and megabase-size telomeric deletions. This aberrant mutational mechanism, present in at least 8% of all HCC tumours, can provide the driver rearrangements that a cancer clone requires to survive and grow, including loss of relevant tumour suppressor genes. Most of these events are clonal and occur early during liver cancer evolution. Real-time timing estimation reveals some HBV-mediated rearrangements occur as early as two decades before cancer diagnosis. Overall, these data underscore the importance of characterising liver cancer genomes for patterns of HBV integration.