The comprehensive relations between healthy adult human brain white matter (WM) microstructure and gray matter (GM) function, and their joint relations to cognitive performance, remain poorly understood. We investigated these associations in 27 younger and 28 older healthy adults by linking diffusion tensor imaging (DTI) with functional magnetic resonance imaging (fMRI) data collected during an n-back working memory task. We present a novel application of multivariate Partial Least Squares (PLS) analysis that permitted the simultaneous modeling of relations between WM integrity values from all major WM tracts and patterns of condition-related BOLD signal across all GM regions. Our results indicate that greater microstructural integrity of the major WM tracts was negatively related to condition-related blood oxygenation level-dependent (BOLD) signal in task-positive GM regions. This negative relationship suggests that better quality of structural connections allows for more efficient use of task-related GM processing resources. Individuals with more intact WM further showed greater BOLD signal increases in typical "task-negative" regions during fixation, and notably exhibited a balanced magnitude of BOLD response across task-positive and -negative states. Structure-function relations also predicted task performance, including accuracy and speed of responding. Finally, structure-function-behavior relations reflected individual differences over and above chronological age. Our findings provide evidence for the role of WM microstructure as a scaffold for the context-relevant utilization of GM regions.