Despite interindividual differences in cortical structure, cross-sectional and longitudinal studies have demonstrated a large degree of population-level consistency in age-related differences in brain morphology. This study assessed how accurately an individual's age could be predicted by estimates of cortical morphology, comparing a variety of structural measures, including thickness, gyrification and fractal dimensionality. Structural measures were calculated across up to seven different parcellation approaches, ranging from one region to 1000 regions. The age prediction framework was trained using morphological measures obtained from T1-weighted MRI volumes collected from multiple sites, yielding a training dataset of 1056 healthy adults, aged 18-97. Age predictions were calculated using a machine-learning approach that incorporated nonlinear differences over the lifespan. In two independent, held-out test samples, age predictions had a median error of 6-7 years. Age predictions were best when using a combination of cortical metrics, both thickness and fractal dimensionality. Overall, the results reveal that age-related differences in brain structure are systematic enough to enable reliable age prediction based on metrics of cortical morphology.