Characterizing cortical plasticity becomes increasingly important for identifying compensatory mechanisms and structural reserve in the ageing population. While cortical thickness (CT) largely contributed to systems neuroscience, it incompletely informs about the underlying neuroplastic pathophysiology. In turn, microstructural characteristics may correspond to atrophy mechanisms in a more sensitive way. Fractional anisotropy, a diffusion tensor imaging (DTI) measure, is inversely related to cortical histologic complexity. Axial diffusivity and radial diffusivity are assumed to be linked to the density of structures oriented perpendicular and parallel to the cortical surface, respectively. We hypothesized (1) that cortical DTI will reveal microstructural correlates for hemispheric specialization, particularly in the language and motor systems, and (2) that lateralization of cortical DTI parameters will show an age effect, paralleling age‐related changes in activation, especially in the prefrontal cortex. We analysed data from healthy younger and older adult participants (N = 91). DTI and CT data were extracted from regions of the Destrieux atlas. Diffusion measures showed lateralization in specialized motor, language, visual, auditory and inferior parietal cortices. Age‐dependent increased lateralization for DTI measures was observed in the prefrontal, angular, superior temporal and lateral occipital cortex. CT did not show any age‐dependent alterations in lateralization. Our observations argue that cortical DTI can capture microstructural properties associated with functional specialization, resembling findings from histology. Age effects on diffusion measures in the integrative prefrontal and parietal areas may shed novel light on the atrophy‐related plasticity in healthy ageing.