Sex chromosome aneuploidy (SCA) increases the risk for cognitive deficits, and confers changes in regional cortical thickness (CT) and surface area (SA). Neuroanatomical correlates of inter-individual variation in cognitive ability have been described in health, but are not well-characterized in SCA. Here, we modeled relationships between general cognitive ability (estimated using full-scale IQ [FSIQ] from Wechsler scales) and regional estimates of SA and CT (from structural MRI scans) in both aneuploid (28 XXX, 55 XXY, 22 XYY, 19 XXYY) and typically-developing euploid (79 XX, 85 XY) individuals. Results indicated widespread decoupling of normative anatomical-cognitive relationships in SCA: we found five regions where SCA significantly altered SA-FSIQ relationships, and five regions where SCA significantly altered CT-FSIQ relationships. The majority of areas were characterized by the presence of positive anatomy-IQ relationships in health, but no or slightly negative anatomy-IQ relationships in SCA. Disrupted anatomical-cognitive relationships generalized from the full cohort to karyotypically defined subcohorts (i.e., XX-XXX; XY-XYY; XY-XXY), demonstrating continuity across multiple supernumerary SCA conditions. As the first direct evidence of altered regional neuroanatomical-cognitive relationships in supernumerary SCA, our findings shed light on potential genetic and structural correlates of the cognitive phenotype in SCA, and may have implications for other neurogenetic disorders.