The genomic complexity of profound copy number aberrations has prevented effective molecular stratification of ovarian cancers. Here, to decode this complexity, we derived copy number signatures from shallow whole-genome sequencing of 117 high-grade serous ovarian cancer (HGSOC) cases, which were validated on 527 independent cases. We show that HGSOC comprises a continuum of genomes shaped by multiple mutational processes that result in known patterns of genomic aberration. Copy number signature exposures at diagnosis predict both overall survival and the probability of platinum-resistant relapse. Measurement of signature exposures provides a rational framework to choose combination treatments that target multiple mutational processes.