The mutation risk of a DNA locus depends on its oligonucleotide context. In turn, mutability of oligonucleotides varies across individuals, due to exposure to mutagenic agents or due to variable efficiency and/or accuracy of DNA repair. Such variability is captured by mutational signatures, a mathematical construct obtained by a deconvolution of mutation frequency spectra across individuals. There is a need to enhance methods for inferring mutational signatures to make better use of sparse mutation data (e.g., resulting from exome sequencing of cancers), to facilitate insight into underlying biological mechanisms, and to provide more accurate mutation rate baselines for inferring positive and negative selection. We propose a conceptualization of mutational signatures that represents oligonucleotides via descriptors of DNA conformation: base pair, base pair step, and minor groove width parameters. We demonstrate how such DNA structural parameters can accurately predict mutation occurrence due to DNA repair failures or due to exposure to diverse mutagens such as radiation, chemical exposure, and the APOBEC cytosine deaminase enzymes. Furthermore, the mutation frequency of DNA oligomers classed by structural features can accurately capture systematic variability in mutagenesis of >1,000 tumors originating from diverse human tissues. A nonnegative matrix factorization was applied to mutation spectra stratified by DNA structural features, thereby extracting novel mutational signatures. Moreover, many of the known trinucleotide signatures were associated with an additional spectrum in the DNA structural descriptor space, which may aid interpretation and provide mechanistic insight. Overall, we suggest that the power of DNA sequence motif-based mutational signature analysis can be enhanced by drawing on DNA shape features.