Somatic mutations in driver genes may ultimately lead to the development of cancer. Understanding how somatic mutations accumulate in cancer genomes and the underlying factors that generate somatic mutations is therefore crucial for developing novel therapeutic strategies. To understand the interplay between spatial genome organization and specific mutational processes, we studied 3,000 tumor-normal-pair whole-genome datasets from 42 different human cancer types. Our analyses reveal that the change in somatic mutational load in cancer genomes is co-localized with topologically-associating-domain boundaries. Domain boundaries constitute a better proxy to track mutational load change than replication timing measurements. We show that different mutational processes lead to distinct somatic mutation distributions where certain processes generate mutations in active domains, and others generate mutations in inactive domains. Overall, the interplay between three-dimensional genome organization and active mutational processes has a substantial influence on the large-scale mutation-rate variations observed in human cancers.