Interhemispheric anatomical differences have long been thought to be related to language lateralisation. Previous studies have explored whether asymmetries in the diffusion characteristics of white matter language tracts are consistent with language lateralisation. These studies, typically with smaller cohorts, yielded mixed results. This study investigated whether connectomic analysis of quantitative anisotropy (QA) and shape features of white matter tracts across the whole brain are associated with language lateralisation. We analysed 1040 healthy individuals (562 females) from the Human Connectome Project database. Hemispheric language dominance for each participant was quantified using a laterality quotient (LQ) derived from fMRI activation in regions of interest (ROIs) associated with a language comprehension task compared against a math task. A linear regression model was used to examine the relationship between structural asymmetry and functional lateralisation. Connectometry revealed a significant negative correlation between LQs and QA of corpus callosum tracts, indicating that higher QA in these regions is associated with bilateral and right-hemisphere language representation in frontal and temporal regions, respectively. Left language laterality in temporal lobe was significantly associated with longer right inferior fronto-occipital fasciculus (IFOF) and forceps minor tracts. These results suggest that diffusion measures of microstructural architecture as well as geometrical features of reconstructed white matter tracts play a role in language lateralisation. People with increased dependence on right or both frontal hemispheres for language processing may have more developed commissural fibres, which may support more efficient interhemispheric communication.Significance statement The left cerebral hemisphere is dominant for language functions in most people. In some healthy people, language functions are lateralised to the right hemisphere or distributed across both hemispheres. The anatomy underlying patterns of hemispheric language dominance are not well established. Emerging evidence suggests that white matter connectivity and architecture is an important feature of cortical functional organisation. In this work, we report that people who have language functions distributed across both hemispheres have greater inter-hemispheric connectivity compared to lateralised people. Our findings provide further insights into the anatomical basis of language function and may have wider clinical implications.