Altered basal ganglia and thalamic connectivity may be critical for cognitive, motor and behavioural impairments common to very preterm (<32 weeks' gestational age) children. This study aims to (1) compare corticostriatal and thalamocortical tract connectivity between very preterm and term-born children at 7 years of age; (2) explore tract connectivity associations with 7-year neurodevelopmental outcomes, and whether these relationships differed between groups. Eighty-three very preterm and 19 term-born (≥37 weeks' gestational age) children underwent structural and diffusion magnetic resonance imaging and had a neuropsychological assessment at 7 years. Corticostriatal and thalamocortical tracts were reconstructed and white matter connectivity was estimated with apparent fibre density. Compared with term-born controls, very preterm children had decreased connectivity in tracts linking the caudate to right motor areas (-10%, p = 0.03) and the thalamus with left motor areas (-5.7%, p = 0.03). Reduced connectivity in corticostriatal and thalamocortical tracts was associated with adverse motor functioning in both groups (p = 0.06). Decreased connectivity of the left caudate and putamen with the lateral prefrontal cortex was associated with lower reading performance for controls (p = 0.06). Corticostriatal and thalamocortical tracts are vulnerable to very preterm birth. Poorer connectivity in these tracts may underlie the motor impairments observed in very preterm children.