The preservation of near-typical function in distributed brain networks is associated with less severe deficits in chronic stroke patients. However, it remains unclear how task-evoked responses in networks that support complex cognitive functions such as semantic processing relate to the post-stroke brain anatomy. Here, we used recently developed methods for the analysis of multimodal MRI data to investigate the relationship between regional tissue concentration and functional MRI activation evoked during auditory semantic decisions in a sample of 43 chronic left hemispheric stroke patients and 43 age, handedness, and sex-matched controls. Our analyses revealed that closer-to-normal levels of tissue concentration in left temporo-parietal cortex and the underlying white matter correlated with the level of task-evoked activation in distributed regions associated with the semantic network. This association was not attributable to the effects of left hemispheric lesion or brain volumes, and similar results were obtained when using explicit lesion data. Left temporo-parietal tissue concentration and the associated task-evoked activations predicted patient performance on the in-scanner task, and also predicted patient performance on out-of-scanner naming and verbal fluency tasks. Exploratory analyses using the average HCP-842 tractography dataset revealed the presence of fronto-temporal, fronto-parietal, and temporo-parietal semantic network connections in the locations where tissue concentration was found to correlate with task-evoked activation in the semantic network. In summary, our results link the preservation of left posterior temporo-parietal structures with the preservation of task-evoked semantic network function in chronic left hemispheric stroke patients. Speculatively, this relationship may reflect the status of posterior temporo-parietal areas as cortical and white matter convergence zones that support coordinated processing in the distributed semantic network. Damage to these regions may contribute to atypical task-evoked responses during semantic processing in chronic stroke patients.