Advanced age is the main risk factor for most chronic diseases and functional deficits in humans, but the fundamental mechanisms that drive ageing remain largely unknown, impeding the development of interventions that might delay or prevent age-related disorders and maximize healthy lifespan. Cellular senescence, which halts the proliferation of damaged or dysfunctional cells, is an important mechanism to constrain the malignant progression of tumour cells1,2. Senescent cells accumulate in various tissues and organs with ageing3 and have been hypothesized to disrupt tissue structure and function because of the components they secrete4,5. However, whether senescent cells are causally implicated in age-related dysfunction and whether their removal is beneficial has remained unknown. To address these fundamental questions, we made use of a biomarker for senescence, p16Ink4a, to design a novel transgene, INK-ATTAC, for inducible elimination of p16Ink4a-positive senescent cells upon administration of a drug. Here we show that in the BubR1 progeroid mouse background, INK-ATTAC removes p16Ink4a-positive senescent cells upon drug treatment. In tissues—such as adipose tissue, skeletal muscle and eye—in which p16Ink4a contributes to the acquisition of age-related pathologies, life-long removal of p16Ink4a-expressing cells delayed onset of these phenotypes. Furthermore, late-life clearance attenuated progression of already established age-related disorders. These data indicate that cellular senescence is causally implicated in generating age-related phenotypes and that removal of senescent cells can prevent or delay tissue dysfunction and extend healthspan.