A comprehensive catalogue of the mutations that drive tumorigenesis and progression is essential to understanding tumor biology and developing therapies. Protein-coding driver mutations have been well-characterized by large exome-sequencing studies, however many tumors have no mutations in protein-coding driver genes. Non-coding mutations are thought to explain many of these cases, however few non-coding drivers besides TERT promoter are known. To fill this gap, we analyzed 150,000 cis-regulatory regions in 1,844 whole cancer genomes from the ICGC-TCGA PCAWG project. Using our new method, ActiveDriverWGS, we found 41 frequently mutated regulatory elements (FMREs) enriched in non-coding SNVs and indels (FDR<0.05) characterized by aging-associated mutation signatures and frequent structural variants. Most FMREs are distal from genes, reported here for the first time and also recovered by additional driver discovery methods. FMREs were enriched in super-enhancers, H3K27ac enhancer marks of primary tumors and long-range chromatin interactions, suggesting that the mutations drive cancer by distally controlling gene expression through three-dimensional genome organization. In support of this hypothesis, the chromatin interaction network of FMREs and target genes revealed associations of mutations and differential gene expression of known and novel cancer genes (e.g., CNNB1IP1, RCC1), activation of immune response pathways and altered enhancer marks. Thus distal genomic regions may include additional, infrequently mutated drivers that act on target genes via chromatin loops. Our study is an important step towards finding such regulatory regions and deciphering the somatic mutation landscape of the non-coding genome.