The human adult structural connectome has a rich topology composed of nodal hierarchies containing highly diverse connectivity patterns, aligned to the diverse range of functional specialisations in the brain. The emergence of this hierarchical complexity in human development is unknown. Here, we substantiate the hierarchical tiers and complexity of brain networks in the newborn period, assess correspondences with hierarchical complexity in adulthood, and investigate the effect of preterm birth, a leading cause of neurocognitive impairment and atypical brain development, on hierarchical complexity. We report that the neonatal and adult structural connectomes are both composed of distinct hierarchical tiers. Consistency of ROIs is found at both ends of this hierarchy during early life and in adulthood, but significant differences are evident in intermediate tiers. The neonatal connectome is hierarchically complex in term born neonates, but hierarchically complexity is altered in association with preterm birth. This is mainly due to diversity of connectivity patterns in Tier 3, which is comprised of regions that underlie sensorimotor processing and its integration with cognitive information. For neonates and adults, the highest tier (comprising hub regions) is ordered, rather than complex, with more homogeneous connectivity patterns in structural hubs. This suggests that the brain develops first a more rigid hierarchical structure in hub regions allowing for the development of greater and more diverse functional specialisation in lower level regions, while connectivity underpinning this diversity is dysmature in infants born preterm.