Identifying driver genes from somatic mutations is a central problem in cancer biology. Existing methods, however, either lack explicit statistical models, or use models based on simplistic assumptions. Here, we present driverMAPS (Model-based Analysis of Positive Selection), a model-based approach to driver gene identification. This method explicitly models positive selection at the single-base level, as well as highly heterogeneous background mutational processes. In particular, the selection model captures elevated mutation rates in functionally important sites using multiple external annotations, and spatial clustering of mutations. Simulations under realistic evolutionary models demonstrate the increased power of driverMAPS over current approaches. Applying driverMAPS to TCGA data of 20 tumor types, we identified 159 new potential driver genes, including the mRNA methyltransferase METTL3-METTL14. We experimentally validated METTL3 as a tumor suppressor gene in bladder cancer, providing support to the important role mRNA modification plays in tumorigenesis.