Children born very preterm (<32 weeks gestational age) are known to be at increased risk of neurocognitive impairments, in domains including executive functioning, processing speed, and fluid and crystallised intelligence. Given the close association between these constructs, the current study investigated a specific model, namely whether executive functioning and/or processing speed mediates the relationship between preterm birth and intelligence. Participants were 204 children born very preterm and 98 full-term children, who completed a battery of tasks measuring executive functioning, processing speed, and fluid and crystallised intelligence. Independent-samples t-tests found significantly poorer performance by children born preterm on all measures, and a confirmatory factor analysis found preterm birth to be significantly related to each of the cognitive domains. A latent-variable mediation model found that executive functioning fully mediated the associations between preterm birth and both fluid and crystallised intelligence. Processing speed fully mediated the preterm birth-fluid intelligence association, but only partially mediated the preterm birth-crystallised intelligence association. Future research should consider a longitudinal study design to test whether these deficits and mediating effects remain throughout childhood and adolescence.