During ageing, muscle stem-cell regenerative function declines. At advanced geriatric age, this decline is maximal owing to transition from a normal quiescence into an irreversible senescence state. How satellite cells maintain quiescence and avoid senescence until advanced age remains unknown. Here we report that basal autophagy is essential to maintain the stem-cell quiescent state in mice. Failure of autophagy in physiologically aged satellite cells or genetic impairment of autophagy in young cells causes entry into senescence by loss of proteostasis, increased mitochondrial dysfunction and oxidative stress, resulting in a decline in the function and number of satellite cells. Re-establishment of autophagy reverses senescence and restores regenerative functions in geriatric satellite cells. As autophagy also declines in human geriatric satellite cells, our findings reveal autophagy to be a decisive stem-cell-fate regulator, with implications for fostering muscle regeneration in sarcopenia.