Age-related changes in DNA methylation (DNAm) form the basis for the development of most robust predictors of age, epigenetic clocks, but a clear mechanistic basis for what exactly they quantify is lacking. Here, to clarify the nature of epigenetic aging, we analyzed the aging dynamics of bulk-tissue and single-cell DNAm, together with single-cell DNAm changes during early development. We show that aging DNAm changes are widespread, but are relatively slow and small in amplitude, with DNAm levels trending towards intermediate values and showing increased heterogeneity with age. By considering dominant types of DNAm changes, we find that aging manifests in the exponential decay-like loss or gain of methylation with a universal rate, independent of the initial level of DNAm. We further show that aging is dominated by the stochastic component, yet co-regulated changes are also present during both development and adulthood. We support the finding of stochastic epigenetic aging by direct single-cell DNAm analyses and modeling of aging DNAm trajectories with a stochastic process akin to radiocarbon decay. Finally, we describe a single-cell algorithm for the identification of co-regulated CpG clusters that may provide new opportunities for targeting aging and evaluating longevity interventions.