Telomere length (TL) is considered an important biomarker of whole-organism health and ageing. Across humans and other vertebrates, short telomeres are associated with increased subsequent mortality risk, but the processes responsible for this correlation remain uncertain. A key unanswered question is whether TL–mortality associations arise due to positive effects of genes or early-life environment on both an individual’s average lifetime TL and their longevity, or due to more immediate effects of environmental stressors on within-individual TL loss and increased mortality risk. Addressing this question requires longitudinal TL and life-history data across the entire lifetimes of many individuals, which are difficult to obtain for long-lived species like humans. Using longitudinal data and samples collected over nearly two decades, as part of a long-term study of wild Soay sheep, we dissected an observed positive association between TL and subsequent survival using multivariate quantitative genetic models. We found no evidence that telomere attrition was associated with increased mortality risk, suggesting that TL is not an important marker of biological ageing or exposure to environmental stress in our study system. Instead, we find that among-individual differences in average TL are associated with increased lifespan. Our47 analyses suggest that this correlation between an individual’s average TL and lifespan has a genetic basis. This demonstrates that TL has the potential to evolve under natural conditions, and suggests an important role of genetics underlying the widespread observation that short telomeres predict mortality.