The possibility to sequence DNA in cancer samples has triggered much effort recently to identify the forces at the genomic level that shape tumorigenesis and cancer progression. It has resulted in novel understanding or clarification of two important aspects of cancer genomics: (i) intra-tumor heterogeneity (ITH), as captured by the variability in observed prevalences of somatic mutations within a tumor, and (ii) mutational processes, as revealed by the distribution of the types of somatic mutation and their immediate nucleotide context. These two aspects are not independent from each other, as different mutational processes can be involved in different subclones, but current computational approaches to study them largely ignore this dependency. In particular, sequential methods that first estimate subclones and then analyze the mutational processes active in each clone can easily miss changes in mutational processes if the clonal decomposition step fails, and conversely information regarding mutational signatures is overlooked during the subclonal reconstruction. To address current limitations, we present CloneSig, a new computational method to jointly infer ITH and mutational processes in a tumor from bulk-sequencing data, including whole-exome sequencing (WES) data, by leveraging their dependency. We show through an extensive benchmark on simulated samples that CloneSig is always as good as or better than state-of-the-art methods for ITH inference and detection of mutational processes. We then apply CloneSig to a large cohort of 8,954 tumors with WES data from the cancer genome atlas (TCGA), where we obtain results coherent with previous studies on whole-genome sequencing (WGS) data, as well as new promising findings. This validates the applicability of CloneSig to WES data, paving the way to its use in a clinical setting where WES is increasingly deployed nowadays.