Age-related tissue alterations have been associated with a decline in stem cell number and function. Although increased cell-to-cell variability in transcription or epigenetic marks has been proposed to be a major hallmark of ageing, little is known about the molecular diversity of stem cells during ageing. Here we present a single cell multi-omics study of mouse muscle stem cells, combining single-cell transcriptome and DNA methylome profiling. Aged cells show a global increase of uncoordinated transcriptional heterogeneity biased towards genes regulating cell-niche interactions. We find context-dependent alterations of DNA methylation in aged stem cells. Importantly, promoters with increased methylation heterogeneity are associated with increased transcriptional heterogeneity of the genes they drive. These results indicate that epigenetic drift, by accumulation of stochastic DNA methylation changes in promoters, is associated with the degradation of coherent transcriptional networks during stem cell ageing. Furthermore, our observations also shed light on the mechanisms underlying the DNA methylation clock.