Advances in neonatal medicine have resulted in a larger proportion of preterm-born individuals reaching adulthood. Their increased liability to psychiatric illness and impairments of cognition and behaviour intimate lasting cerebral consequences; however, the central physiological disturbances remain unclear. Of fundamental importance to efficient brain function is the coordination and contextually-relevant recruitment of neural networks. Large-scale distributed networks emerge perinatally and increase in hierarchical complexity through development. Preterm-born individuals exhibit systematic reductions in correlation strength within these networks during infancy. Here, we investigate resting-state functional connectivity in functional magnetic resonance imaging data from 29 very-preterm (VPT)-born adults and 23 term-born controls. Neurocognitive networks were identified with spatial independent component analysis conducted using the Infomax algorithm and employing Icasso procedures to enhance component robustness. Network spatial focus and spectral power were not generally significantly affected by preterm birth. By contrast, Granger-causality analysis of the time courses of network activity revealed widespread reductions in between-network connectivity in the preterm group, particularly along paths including salience-network features. The potential clinical relevance of these Granger-causal measurements was suggested by linear discriminant analysis of topological representations of connection strength, which classified individuals by group with a maximal accuracy of 86%. Functional connections from the striatal salience network to the posterior default mode network informed this classification most powerfully. In the VPT-born group it was additionally found that perinatal factors significantly moderated the relationship between executive function (which was reduced in the VPT-born as compared with the term-born group) and generalised partial directed coherence. Together these findings show that resting-state functional connectivity of preterm-born individuals remains compromised in adulthood; and present consistent evidence that the striatal salience network is preferentially affected. Therapeutic practices directed at strengthening within-network cohesion and fine-tuning between-network inter-relations may have the potential to mitigate the cognitive, behavioural and psychiatric repercussions of preterm birth.