Abstract Background and aims Observational studies have linked elevated blood pressure (BP) to impaired cognitive function. However, the functional and structural changes in the brain that mediate the relationship between BP elevation and cognitive impairment remain unknown. Using observational and genetic data from large consortia, this study aimed to identify brain structures potentially associated with BP values and cognitive function. Methods and results Data on BP were integrated with 3935 brain magnetic resonance imaging-derived phenotypes (IDPs) and cognitive function defined by fluid intelligence score. Observational analyses were performed in the UK Biobank and a prospective validation cohort. Mendelian randomisation (MR) analyses used genetic data derived from the UK Biobank, International Consortium for Blood Pressure, and COGENT consortium. Mendelian randomisation analysis identified a potentially adverse causal effect of higher systolic BP on cognitive function [−0.044 standard deviation (SD); 95% confidence interval (CI) −0.066, −0.021] with the MR estimate strengthening (−0.087 SD; 95% CI −0.132, −0.042), when further adjusted for diastolic BP. Mendelian randomisation analysis found 242, 168, and 68 IDPs showing significant (false discovery rate P < 0.05) association with systolic BP, diastolic BP, and pulse pressure, respectively. Most of these IDPs were inversely associated with cognitive function in observational analysis in the UK Biobank and showed concordant effects in the validation cohort. Mendelian randomisation analysis identified relationships between cognitive function and the nine of the systolic BP-associated IDPs, including the anterior thalamic radiation, anterior corona radiata, or external capsule. Conclusion Complementary MR and observational analyses identify brain structures associated with BP, which may be responsible for the adverse effects of hypertension on cognitive performance.