Schizophrenia is characterized by abnormal brain structure such as global reductions in gray matter volume. Machine learning models trained to estimate the age of brains from structural neuroimaging data consistently show advanced brain-age to be associated with schizophrenia. Yet, it is unclear whether advanced brain-age is specific to schizophrenia compared to other psychotic disorders, and whether evidence that brain structure is “older” than chronological age actually reflects neurodevelopmental rather than atrophic processes. It is also unknown whether advanced brain-age is associated with genetic liability for psychosis carried by biological relatives of people with schizophrenia. We used the Brain-Age Regression Analysis and Computation Utility Software (BARACUS) prediction model and calculated the residualized brain-age gap of 332 adults (163 individuals with psychotic disorders: 105 schizophrenia, 17 schizoaffective disorder, 41 bipolar I disorder with psychotic features; 103 first-degree biological relatives; 66 controls). The model estimated advanced brain-ages for people with psychosis in comparison to controls and relatives, with no differences among psychotic disorders or between relatives and controls. Specifically, the model revealed an enlarged brain-age gap for schizophrenia and bipolar disorder with psychotic features. Advanced brain-age was associated with lower cognitive and general functioning in the full sample. Among relatives, cognitive performance and schizotypal symptoms were related to brain-age gap, suggesting that advanced brain-age is associated with the subtle expressions associated with psychosis. Exploratory longitudinal analyses suggested that brain aging was not accelerated in individuals with a psychotic disorder. In sum, we found that people with psychotic disorders, irrespective of specific diagnosis or illness severity, show indications of non-progressive, advanced brain-age. These findings support a transdiagnostic, neurodevelopmental formulation of structural brain abnormalities in psychotic psychopathology.