The involvement of the right hemisphere (RH) in language, and especially after aphasia resulting from left hemisphere (LH) lesions, has been recently highlighted. The present study investigates white matter structure in the right hemisphere of 25 chronic post-stroke aphasic patients after LH lesions in comparison with 24 healthy controls, focusing on the four cortico-cortical tracts that link posterior parietal and temporal language-related areas with Broca’s region in the inferior frontal gyrus of the LH: the Superior Longitudinal Fasciculi II and III (SLF II and SLF III), the Arcuate Fasciculus (AF), and the Temporo-Frontal extreme capsule Fasciculus (TFexcF). Additionally, the relationship of these RH white matter tracts to language performance was examined. The patients with post-stroke aphasia in the chronic phase and the healthy control participants underwent diffusion tensor imaging (DTI) examination. The aphasic patients were assessed with standard aphasia tests. The results demonstrated increased axial diffusivity in the RH tracts of the aphasic patients. Patients were then divided according to the extent of the left hemisphere white matter loss. Correlations of language performance with radial diffusivity (RD) in the right hemisphere homologs of the tracts examined were demonstrated for the TFexcF, SLF III, and AF in the subgroup with limited damage to the LH language networks and only with the TFexcF in the subgroup with extensive damage. The results argue in favor of compensatory roles of the right hemisphere tracts in language functions when the LH networks are disrupted.