Somatic mutations in human cancers show unevenness in genomic distribution that correlate with aspects of genome structure and function. These mutations are, however, generated by multiple mutational processes operating through the cellular lineage between the fertilized egg and the cancer cell, each composed of specific DNA damage and repair components and leaving its own characteristic mutational signature on the genome. Using somatic mutation catalogues from 560 breast cancer whole-genome sequences, here we show that each of 12 base substitution, 2 insertion/deletion (indel) and 6 rearrangement mutational signatures present in breast tissue, exhibit distinct relationships with genomic features relating to transcription, DNA replication and chromatin organization. This signature-based approach permits visualization of the genomic distribution of mutational processes associated with APOBEC enzymes, mismatch repair deficiency and homologous recombinational repair deficiency, as well as mutational processes of unknown aetiology. Furthermore, it highlights mechanistic insights including a putative replication-dependent mechanism of APOBEC-related mutagenesis.