Epigenetic alterations such as promoter hypermethylation may drive cancer through tumor suppressor genes inactivation. However, we have limited ability to differentiate driver DNA methylation (DNAme) changes from passenger events. We developed DNAme driver inference - MethSig - accounting for the varying stochastic hypermethylation rate across the genome and between samples. We applied MethSig to bisulfite sequencing data of chronic lymphocytic leukemia (CLL), multiple myeloma, ductal carcinoma in situ, glioblastoma, and to methylation array data across 18 tumor types in TCGA. MethSig resulted in well-calibrated Quantile-Quantile plots and reproducible inference of likely DNAme drivers with increased sensitivity/specificity compared to benchmarked methods. CRISPR/Cas9 knockout of selected candidate CLL DNAme drivers provided a fitness advantage with and without therapeutic intervention. Notably, DNAme driver risk score was closely associated with adverse outcome in independent CLL cohorts. Collectively, MethSig represents a novel inference framework for DNAme driver discovery to chart the role of aberrant DNAme in cancer.