Extensive improvements in executive functions and language abilities are accompanied by changes in functional connections within the brain and in gray and white matter during the first few years of life. Diffusion tensor imaging provides a unique look into pediatric brain anatomy and critical information regarding white-matter development. The aims of the current study were to investigate the variability in diffusion indices in language and cognitive white-matter tracts, hemispheric lateralization, and how diffusion measures are related to age, language and cognitive abilities from early toddler age to early childhood. Diffusion tensor imaging data were acquired from seventy-four 17–107 month-old typically developing children (mean = 69 months; females = 39). Effects of hemisphere and age on diffusion properties (mean diffusivity, radial diffusivity, axial diffusivity and fractional anisotropy) were measured at 100 points along the length of white-matter tracts related to expressive language and cognitive abilities, including the cingulum bundle, superior longitudinal fasciculus, inferior longitudinal fasciculus, inferior fronto-occipital fasciculus, arcuate fasciculus and corpus callosum (forceps major and forceps minor). Diffusion properties exhibited variability along the length of the tracts, with hemispheric effect and age differences in specific segments of the tracts. Significant positive correlation was found between fractional anisotropy and expressive language and cognitive abilities. Our results provide a detailed examination of the effect of age and hemisphere on diffusion properties. Furthermore, the results delineate the neural correlates of white-matter microstructure to behavioral language and cognitive performance in white-matter tracts related to language and cognitive abilities at the tract level along with development.