Abstract Objectives To examine whether educational attainment and intelligence have causal effects on risk of Alzheimer’s disease (AD), independently of each other. Design Two-sample univariable and multivariable Mendelian randomization (MR) to estimate the causal effects of education on intelligence and vice versa, and the total and independent causal effects of both education and intelligence on AD risk. Participants 17 008 AD cases and 37 154 controls from the International Genomics of Alzheimer’s Project (IGAP) consortium. Main outcome measure Odds ratio (OR) of AD per standardized deviation increase in years of schooling (SD = 3.6 years) and intelligence (SD = 15 points on intelligence test). Results There was strong evidence of a causal, bidirectional relationship between intelligence and educational attainment, with the magnitude of effect being similar in both directions [OR for intelligence on education = 0.51 SD units, 95% confidence interval (CI): 0.49, 0.54; OR for education on intelligence = 0.57 SD units, 95% CI: 0.48, 0.66]. Similar overall effects were observed for both educational attainment and intelligence on AD risk in the univariable MR analysis; with each SD increase in years of schooling and intelligence, odds of AD were, on average, 37% (95% CI: 23–49%) and 35% (95% CI: 25–43%) lower, respectively. There was little evidence from the multivariable MR analysis that educational attainment affected AD risk once intelligence was taken into account (OR = 1.15, 95% CI: 0.68–1.93), but intelligence affected AD risk independently of educational attainment to a similar magnitude observed in the univariate analysis (OR = 0.69, 95% CI: 0.44–0.88). Conclusions There is robust evidence for an independent, causal effect of intelligence in lowering AD risk. The causal effect of educational attainment on AD risk is likely to be mediated by intelligence.