Focal chromosomal amplification contributes to the initiation of cancer by mediating overexpression of oncogenes1-3, and to the development of cancer therapy resistance by increasing the expression of genes whose action diminishes the efficacy of anti-cancer drugs. Here we used whole-genome sequencing of clonal cell isolates that developed chemotherapeutic resistance to show that chromothripsis is a major driver of circular extrachromosomal DNA (ecDNA) amplification (also known as double minutes) through mechanisms that depend on poly(ADP-ribose) polymerases (PARP) and the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs). Longitudinal analyses revealed that a further increase in drug tolerance is achieved by structural evolution of ecDNAs through additional rounds of chromothripsis. In situ Hi-C sequencing showed that ecDNAs preferentially tether near chromosome ends, where they re-integrate when DNA damage is present. Intrachromosomal amplifications that formed initially under low-level drug selection underwent continuing breakage-fusion-bridge cycles, generating amplicons more than 100 megabases in length that became trapped within interphase bridges and then shattered, thereby producing micronuclei whose encapsulated ecDNAs are substrates for chromothripsis. We identified similar genome rearrangement profiles linked to localized gene amplification in human cancers with acquired drug resistance or oncogene amplifications. We propose that chromothripsis is a primary mechanism that accelerates genomic DNA rearrangement and amplification into ecDNA and enables rapid acquisition of tolerance to altered growth conditions.