Chromatin accessibility data can elucidate the developmental origin of cancer cells and reveal the enhancer landscape of key oncogenic transcriptional regulators. We develop a computational strategy called PSIONIC (patient-specific inference of networks informed by chromatin) to combine chromatin accessibility data with large tumor expression data and model the effect of enhancers on transcriptional programs in multiple cancers. We generate a new ATAC-seq data profiling chromatin accessibility in gynecologic and basal breast cancer cell lines and apply PSIONIC to 723 patient and 96 cell line RNA-seq profiles from ovarian, uterine, and basal breast cancers. Our computational framework enables us to share information across tumors to learn patient-specific TF activities, revealing regulatory differences between and within tumor types. PSIONIC-predicted activity for MTF1 in cell line models correlates with sensitivity to MTF1 inhibition, showing the potential of our approach for personalized therapy. Many identified TFs are significantly associated with survival outcome. To validate PSIONIC-derived prognostic TFs, we perform immunohistochemical analyses in 31 uterine serous tumors for ETV6 and 45 basal breast tumors for MITF and confirm that the corresponding protein expression patterns are also significantly associated with prognosis.