Senescence, the process of physiological deterioration associated with growing old, is a shared characteristic of a wide range of animals. Yet, lifespan varies dramatically among species. To explain this variation, the evolutionary theory of ageing has been proposed more than 50 yr ago. Although the theory has been tested experimentally and through comparative analyses, there remains debate whether its fundamental prediction is empirically supported. Here, we use a comprehensive database on avian life history traits to test the evolutionary theory of ageing at a global scale. We show that pronounced geographical gradients of maximum longevity exist, that they are predicted by measures of predator diversity and only partly depend on correlated life-history traits. The results are consistent with species-level analyses and can be replicated across bio-geographical regions. Our analyses suggest that stochastic predation is an important driver of the evolution of lifespan, at least in birds.