Epigenetic changes during ageing have been characterized by multiple epigenetic clocks that allow the prediction of chronological age based on methylation status. Despite their accuracy and utility, epigenetic age biomarkers leave many questions about epigenetic ageing unanswered. Specifically, they do not permit the unbiased characterization of non-linear epigenetic ageing trends across entire life spans, a critical question underlying this field of research. Here we provide an integrated framework to address this question. Our model, inspired from evolutionary models, is able to account for acceleration/deceleration in epigenetic changes by fitting an individual's model age, the epigenetic age, which is related to chronological age in a non-linear fashion. Application of this model to DNA methylation data measured across broad age ranges, from before birth to old age, and from two tissue types, suggests a universal logarithmic trend characterizes epigenetic ageing across entire lifespans.