We examined whether sarcopenia is associated with the occurrence of late-life cognitive impairment.Nondemented older adults (N = 1175) underwent annual testing with 17 cognitive tests summarized as a global cognitive score. A composite sarcopenia score was constructed based on muscle mass measured with bioelectrical impedance and muscle function based on grip strength. Cox proportional hazard models were employed to examine associations of sarcopenia with incident Alzheimer's dementia (AD) and incident mild cognitive impairment (MCI). Linear mixed-effect models determined the association of sarcopenia with cognitive decline. All models controlled for age, sex, education, race, and height squared.Average follow-up was 5.6 years. More severe sarcopenia at baseline was associated with a higher risk of incident AD (hazard ratio [HR], 1.50 [95% confidence interval 1.20-1.86]; p < 0.001) and of MCI (1.21 [1.01-1.45]; 0.04) and a faster rate of cognitive decline (estimate = -0.013; p = 0.01). Analyses of the individual components of sarcopenia showed that muscle function was associated with incident AD, incident MCI, and cognitive decline with and without a term for lean muscle mass in the model. In contrast, lean muscle mass was not associated with incident cognitive impairment or cognitive decline when a term for muscle function was included in the model.Poor muscle function, but not reduced lean muscle mass, drives the association of sarcopenia with late-life cognitive impairment. Further work is needed to identify features of muscle structure, which may increase the specificity of sarcopenia for identifying older adults at risk for late-life cognitive impairment.