Combination therapies offer promise for improving cancer treatment efficacy and preventing recurrence. However, identifying optimal drug combinations tailored to specific cancer subtypes and individual patients is extremely challenging due to the vast number of possible combinations and tumor heterogeneity. To address this gap, we take a machine learning approach combining deep learning with transfer learning to incorporate prior scientific knowledge and predict drug synergy based on tumor-specific transcriptome profiles. This approach, called PAIRWISE, explicitly modeled synergistic effects of drug combinations in cancer cell lines or individual tumor samples based on drug chemical structures, drug targets, and transcriptomes of inferred samples. PAIRWISE outperformed competing models with an area under the receiver operating characteristic curve (AUROC) of 0.85 on held-out cancer cell lines. When applied to an independent dataset of combinations with Bruton Tyrosine Kinase inhibitors (BTKi) in Diffuse Large B Cell Lymphoma (DLBCL) cell lines, PAIRWISE accurately predicted synergistic drug combinations with an AUROC of 0.72. To further confirm the robustness of PAIRWISE predictions, we performed an in silico, patient profile-directed screen for other compounds that would synergize with BTKi in DLBCL patients, and confirmed the synergy of the predictions using a panel of eight non-Hodgkin lymphoma cell lines. These findings demonstrate the ability of PAIRWISE to nominate effective personalized drug combinations, accelerating the development of precision oncology.