Somatic mutations acquired in healthy tissues as we age are major determinants of cancer risk. Whether variants confer a fitness advantage or rise to detectable frequencies by chance remains largely unknown. Blood sequencing data from similar to 50,000 individuals reveal how mutation, genetic drift, and fitness shape the genetic diversity of healthy blood (clonal hematopoiesis). We show that positive selection, not drift, is the major force shaping clonal hematopoiesis, provide bounds on the number of hematopoietic stem cells, and quantify the fitness advantages of key pathogenic variants, at single-nucleotide resolution, as well as the distribution of fitness effects (fitness landscape) within commonly mutated driver genes. These data are consistent with clonal hematopoiesis being driven by a continuing risk of mutations and clonal expansions that become increasingly detectable with age.