General intelligence is a robust predictor of important life outcomes, including educational and occupational attainment, successfully managing everyday life situations, good health and longevity. Some neuronal correlates of intelligence have been discovered, mainly indicating that larger cortices in widespread parieto-frontal brain networks and efficient neuronal information processing support higher intelligence. However, there is a lack of established associations between general intelligence and any basic structural brain parameters that have a clear functional meaning. Here, we provide evidence that lower brain-wide white matter tract integrity exerts a substantial negative effect on general intelligence through reduced information-processing speed. Structural brain magnetic resonance imaging scans were acquired from 420 older adults in their early 70s. Using quantitative tractography, we measured fractional anisotropy and two white matter integrity biomarkers that are novel to the study of intelligence: longitudinal relaxation time (T1) and magnetisation transfer ratio. Substantial correlations among 12 major white matter tracts studied allowed the extraction of three general factors of biomarker-specific brain-wide white matter tract integrity. Each was independently associated with general intelligence, together explaining 10% of the variance, and their effect was completely mediated by information-processing speed. Unlike most previously established neurostructural correlates of intelligence, these findings suggest a functionally plausible model of intelligence, where structurally intact axonal fibres across the brain provide the neuroanatomical infrastructure for fast information processing within widespread brain networks, supporting general intelligence.