The genomic complexity of profound copy-number aberration has prevented effective molecular stratification of ovarian cancers. 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. Measuring signature exposures provides a rational framework to choose combination treatments that target multiple mutational processes.