Identifying associations between interindividual variability in brain structure and behaviour requires large cohorts, multivariate methods, out-of-sample validation and, ideally, out-of-cohort replication. Moreover, the influence of nature vs nurture on brain-behaviour associations should be analysed. We analysed associations between brain structure (grey matter volume, cortical thickness, and surface area) and behaviour (spanning cognition, emotion, and alertness) using regularized canonical correlation analysis and a machine learning framework that tests the generalisability and stability of such associations. The replicability of brain-behaviour associations was assessed in two large, independent cohorts. The load of genetic factors on these associations was analysed with heritability and genetic correlation. We found one heritable and replicable latent dimension linking cognitive-control/executive-functions and positive affect to brain structural variability in areas typically associated with higher cognitive functions, and with areas typically associated with sensorimotor functions. These results revealed a major axis of interindividual behavioural variability linking to a whole-brain structural pattern.