The five-year survival rate of epithelial ovarian cancer (EOC) is approximately 35-40% despite maximal treatment efforts, highlighting a need for stratification biomarkers for personalized treatment. Here we extract 657 quantitative mathematical descriptors from the preoperative CT images of 364 EOC patients at their initial presentation. Using machine learning, we derive a non-invasive summary-statistic of the primary ovarian tumor based on 4 descriptors, which we name "Radiomic Prognostic Vector" (RPV). RPV reliably identifies the 5% of patients with median overall survival less than 2 years, significantly improves established prognostic methods, and is validated in two independent, multi-center cohorts. Furthermore, genetic, transcriptomic and proteomic analysis from two independent datasets elucidate that stromal phenotype and DNA damage response pathways are activated in RPV-stratified tumors. RPV and its associated analysis platform could be exploited to guide personalized therapy of EOC and is potentially transferrable to other cancer types.