We investigated how the microstructure of relevant white matter connections is associated with cortical responsivity and working memory (WM) performance by collecting diffusion tensor imaging and verbal WM functional magnetic resonance imaging data from 29 young adults. We measured cortical responsivity within the frontoparietal WM network as the difference in blood oxygenation level-dependent (BOLD) signal between 3-back and 1-back conditions. Fractional anisotropy served as an index of the integrity of the superior longitudinal fasciculi (SLF), which connect frontal and posterior regions. We found that SLF integrity is associated with better 3-back performance and greater task-related BOLD responsivity. In addition, BOLD responsivity in right premotor cortex reliably mediated the effects of SLF integrity on 3-back performance but did not uniquely predict 3-back performance after controlling for individual differences in SLF integrity. Our results suggest that task-related adjustments of local gray matter processing are conditioned by the properties of anatomical connections between relevant cortical regions. We suggest that the microarchitecture of white matter tracts influences the speed of signal transduction along axons. This in turn may affect signal summation at neural dendrites, action potential firing, and the resulting BOLD signal change and responsivity.