Inferring single-cell compositions and their contributions to global gene expression changes from bulk RNA sequencing (RNA-seq) datasets is a major challenge in oncology. Here we develop Bayesian cell proportion reconstruction inferred using statistical marginalization (BayesPrism), a Bayesian method to predict cellular composition and gene expression in individual cell types from bulk RNA-seq, using patient-derived, scRNA-seq as prior information. We conduct integrative analyses in primary glioblastoma, head and neck squamous cell carcinoma and skin cutaneous melanoma to correlate cell type composition with clinical outcomes across tumor types, and explore spatial heterogeneity in malignant and nonmalignant cell states. We refine current cancer subtypes using gene expression annotation after exclusion of confounding nonmalignant cells. Finally, we identify genes whose expression in malignant cells correlates with macrophage infiltration, T cells, fibroblasts and endothelial cells across multiple tumor types. Our work introduces a new lens to accurately infer cellular composition and expression in large cohorts of bulk RNA-seq data.