Clonal hematopoiesis (CH) arises when hematopoietic stem cells (HSCs) acquire mutations, most frequently in the DNMT3A and TET2 genes, conferring a competitive advantage through mechanisms that remain unclear. To gain insight into how CH mutations enable gradual clonal expansion, we used single-cell multi-omics with high-fidelity genotyping on human CH bone marrow (BM) samples. Most of the selective advantage of mutant cells occurs within HSCs. DNMT3A- and TET2-mutant clones expand further in early progenitors, while TET2 mutations accelerate myeloid maturation in a dose-dependent manner. Unexpectedly, both mutant and non-mutant HSCs from CH samples are enriched for inflammatory and aging transcriptomic signatures, compared with HSCs from non-CH samples, revealing a non-cell-autonomous effect. However, DNMT3A- and TET2-mutant HSCs have an attenuated inflammatory response relative to wild-type HSCs within the same sample. Our data support a model whereby CH clones are gradually selected because they are resistant to the deleterious impact of inflammation and aging.