White matter connectivity supports diverse cognitive demands by efficiently constraining dynamic brain activity. This efficiency can be inferred from network controllability, which represents the ease with which the brain moves between distinct mental states based on white matter connectivity. However, it remains unclear how brain networks support diverse functions at birth, a time of rapid changes in connectivity. Here, we investigate the development of network controllability during the perinatal period and the effect of preterm birth in 521 neonates. We provide evidence that elements of controllability are exhibited in the infant’s brain as early as the third trimester and develop rapidly across the perinatal period. Preterm birth disrupts the development of brain networks and altered the energy required to drive state transitions at different levels. In addition, controllability at birth is associated with cognitive ability at 18 months. Our results suggest network controllability develops rapidly during the perinatal period to support cognitive demands but could be altered by environmental impacts like preterm birth.