•Older age at menopause is associated with better cognition at around 70 years of age.•Visual processing, associative learning, and memory showed the strongest effects.•Life course covariables explained most, but not all, associations. Associations between age at menopause and cognition post-menopause are examined to determine whether relationships are stronger for certain cognitive domains. Women from the Medical Research Council National Survey of Health and Development and its neuroscience sub-study, Insight 46, were included if they had known age at menopause (self-reported via questionnaire) and complete cognitive outcome data at age 69 (n = 746) or at Insight 46 wave I (n = 197). Multivariable linear regression analyses adjusting for life course confounders were run; interactions with menopause type (natural/surgical) and APOE-ε4 status were examined; and the potential contribution of hormone therapy was assessed. Cognitive measures were standardized Addenbrooke's Cognitive Examination - third edition total and sub-domain scores at age 69 (whole cohort) and Preclinical Alzheimer's Cognitive Composite total and sub-test scores at age ~70 (Insight 46). Older age at menopause was associated with better performance across all outcomes, most strongly for the Addenbrooke's Cognitive Examination memory and visuospatial function sub-domains, and the Preclinical Alzheimer's Cognitive Composite digit-symbol substitution test and face-name associative memory examination sub-tests. Adjusting for early-life factors attenuated all effect estimates, driven by childhood cognition, and accounting for menopause type revealed negative confounding for some outcomes. No significant interactions with menopause type or APOE-ε4 status were detected. Further adjustment for hormone therapy did not meaningfully alter the estimated effects. Older age at menopause is associated with better later-life cognitive performance, particularly for visual processing and associative learning and memory domains. Childhood cognition was an important contributor.