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It is hypothesised that structural brain abnormalities in individuals with schizophrenia are associated with aggressive behaviour, but this has not been tested directly. We pooled magnetic resonance imaging and clinical data from 2095 patients and 2861 healthy control subjects across 20 sites of the ENIGMA-Schizophrenia Working Group. Using normative modelling, we quantified individual-level deviations from controls (z-scores) for global and regional grey matter volume and white matter microstructural integrity. Ordinal regression models were used to estimate the associations between these deviations and concurrent aggression (odds ratios [ORs] with 99% confidence intervals [CIs]). In mediation analyses, we examined the roles of positive symptoms - delusions, hallucinations and disorganised thinking - impulsivity and illness insight. Aggression was significantly associated with reductions in total cortical volume (OR [99% CI] = 0.88 [0.78, 0.98], p = 0.003), global white matter integrity (OR [99% CI] = 0.72 [0.59, 0.88], p = 3.50 × 10^-5), dorsolateral prefrontal cortex volume (OR [99% CI] = 0.85 [0.74, 0.97], p = 0.002), inferior parietal lobule volume (OR [99% CI] = 0.76 [0.66, 0.87], p = 2.20 × 10^-7) and internal capsule integrity (OR [99% CI] = 0.76 [0.63, 0.92], p = 2.90 × 10^-4). These associations were robust to adjustment for relevant covariates and partly mediated by positive symptoms and impulsivity. Our findings suggest that the co-occurrence of positive symptoms, impulsivity and aggression in schizophrenia has a neurobiological basis, providing potential targets for therapeutic interventions.