Recent evidence arising from DNA sequencing of healthy human tissues has clearly indicated that our organs accumulate a relevant number of somatic mutations due to normal endogenous mutational processes, in addition to those caused by environmental factors. A deeper understanding of the evolution of this endogenous mutational load is critical for understanding what causes cancer. Here we present a mathematical model of tumor evolution that is able to predict the expected number of endogenous somatic mutations present in various tissue types of a patient at a given age. These predictions are then compared to those observed in patients. We also obtain an improved fitting of the variation in cancer incidence across cancer types, showing that the endogenous mutational processes can explain 4/5 of the variation in cancer risk. Overall, these results offer key insights into cancer etiology, by providing further evidence for the major role these endogenous processes play in cancer.