Age-related decline in cognitive function has been linked to alterations of white matter and functional brain connectivity. With regard to language, aging has been shown to be associated with impaired syntax processing, but the underlying structural and functional correlates are poorly understood. In the present study, we used an artificial grammar learning (AGL) task to determine the ability to extract grammatical rules from new material in healthy older adults. White matter microstructure and resting-state functional connectivity (FC) of task-relevant brain regions were assessed using multimodal magnetic resonance imaging (MRI). AGL performance correlated positively with fractional anisotropy (FA) underlying left and right Brodmann areas (BA) 44/45 and in tracts originating from left BA 44/45. An inverse relationship was found between task performance and FC of left and right BA 44/45, linking lower performance to stronger inter-hemispheric functional coupling. Our results suggest that white matter microstructure underlying specific prefrontal regions and their functional coupling affect acquisition of syntactic knowledge in the aging brain, offering further insight into mechanisms of functional decline in older adults.