Clonal hematopoiesis (CH) arises when a substantial proportion of mature blood cells is derived from a single dominant hematopoietic stem cell lineage. Somatic mutations in candidate driver (CD) genes are thought to be responsible for at least some cases of CH. Using whole-genome sequencing of 11 262 Icelanders, we found 1403 cases of CH by using barcodes of mosaic somatic mutations in peripheral blood, whether or not they have a mutation in a CD gene. We find that CH is very common in the elderly, trending toward inevitability. We show that somatic mutations in TET2, DNMT3A, ASXL1, and PPM1D are associated with CH at high significance. However, known CD mutations were evident in only a fraction of CH cases. Nevertheless, the highly prevalent CH we detect associates with increased mortality rates, risk for hematological malignancy, smoking behavior, telomere length, Y-chromosome loss, and other phenotypic characteristics. Modeling suggests some CH cases could arise in the absence of CD mutations as a result of neutral drift acting on a small population of active hematopoietic stem cells. Finally, we find a germline deletion in intron 3 of the telomerase reverse transcriptase (TERT) gene that predisposes to CH (rs34002450; P = 7.4 × 10⁻¹²; odds ratio, 1.37).