Features of brain asymmetry have been implicated in a broad range of cognitive processes; however, their origins are still poorly understood. Using a new left-right symmetric, spatiotemporal cortical surface atlas, we investigated cortical asymmetries in 442 healthy newborn infants soon after birth, using structural and functional magnetic resonance images from the Developing Human Connectome Project. We identified previously unrecognised structural and functional asymmetries in auditory, visual and sensorimotor cortices, which closely resemble known asymmetries in adults. These findings show that cortical asymmetries are largely determined prenatally and suggest that they may constrain the development of lateralised functions in later life. In adults, deviations in brain asymmetry have been implicated in a broad range of developmental and psychiatric disorders, some of which have been associated with abnormal perinatal neurodevelopment. To test the hypothesis that normal cortical asymmetry is disrupted in the perinatal period by severe environmental stress, we compared cortical asymmetries between the same group of term neonates and 103 preterm neonates imaged at term-equivalent age. No significant differences were seen between these two cohorts, showing that the development of cortical asymmetries proceeds largely unaffected by preterm birth.