The accumulation of somatic DNA mutations is a hallmark of aging in many dividing cells and contributes to carcinogenesis. Here we survey the landscape of somatic single-nucleotide variants (sSNVs) in heart muscle cells (cardiomyocytes) which normally do not proliferate but often become polyploid with age. Using single-cell whole-genome sequencing we analyzed sSNVs from 48 single cardiomyocytes from 10 healthy individuals (ages 0.4 - 82 yrs.). Cardiomyocyte sSNVs increased strikingly with age, at rates faster than reported in many dividing cells, or in non-dividing neurons. Analysis of nucleotide substitution patterns revealed age-related “clock-like” mutational signatures resembling those previously described. However, cardiomyocytes showed distinct mutational signatures that are rare or absent in other cells, implicating failed nucleotide excision repair of oxidative damage and defective mismatch repair (MMR) during aging. A lineage tree of cardiomyocytes, constructed using clonal sSNVs, revealed that some tetraploid (10%) and most cardiomyocytes with higher ploidy (>60%) derive from distinct clonal origins, implicating cell fusion as a mechanism contributing to many polyploid cardiomyocytes. Since age-accumulated sSNVs create dozens of damaging exonic mutations, cell fusion to form multiploid cardiomyocytes may represent an evolutionary mechanism of cellular genetic compensation that minimizes complete knockout of essential genes during aging. The rates and patterns of accumulation of cardiac mutations provide a paradigm to understand the influence of genomic aging on age-related heart disease.