Aging clocks have provided one of the most significant recent breakthroughs in the biology of aging. Such clocks allow the determination of chronological and increasingly also biological age, which is prerequisite for assessing the effectiveness of interventions in the aging process and preventive treatments of age-related diseases. The most advanced aging clocks are based on age-dependent changes in DNA methylation pattern. The reproducibility of such changes over the life course has reinvigorated the debate whether a programmed process underlies aging. A programmed aging process, however, is incompatibly with the evolutionary theory of aging. Aging occurs as a consequence of a vanishing force of selective pressure post-reproduction as no fitness benefit is provided by immortality of the soma. In fact, stochastic events have been observed to increasingly occur during the aging process. Here, we test whether aging clocks could be built with entirely stochastic variation. We find that accumulating stochastic variation is sufficient to accurately predict chronological and biological age. Moreover, current aging clocks are entirely compatible with random alterations in the methylation or transcriptomic patterns. Our analysis unifies the clock measure of aging with the evolutionary theory of aging and predicts that any set of data that have a ground state at the age zero with accumulating stochastic variation could be used for building accurate aging clocks.