The mechanisms behind the evolution of complex genomic amplifications in cancer have remained largely unclear. Using whole-genome sequencing data of the pediatric tumor neuroblastoma, we here identified a type of amplification, termed ‘seismic amplification’, that is characterized by multiple rearrangements and discontinuous copy number levels. Overall, seismic amplifications occurred in 9.9% (274 of 2,756) of cases across 38 cancer types, and were associated with massively increased copy numbers and elevated oncogene expression. Reconstruction of the development of seismic amplification showed a stepwise evolution, starting with a chromothripsis event, followed by formation of circular extrachromosomal DNA that subsequently underwent repetitive rounds of circular recombination. The resulting amplicons persisted as extrachromosomal DNA circles or had reintegrated into the genome in overt tumors. Together, our data indicate that the sequential occurrence of chromothripsis and circular recombination drives oncogene amplification and overexpression in a substantial fraction of human malignancies.