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Previous working memory research has revealed distributed neural representations of task information across cortex. However, how the distributed task representations emerge and communicate with stimulus-specific information to implement flexible goal-directed computations is still unclear. Here, leveraging electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) in human participants along with state space analyses, we provided converging evidence in support of a low-dimensional neural geometry of goal information congruent with a designed task space, which first emerged in frontal cortex during goal maintenance and then transferred to posterior cortex through frontomedial-to-posterior theta coherence for implementation on stimulus-specific representations. Importantly, the fidelity of the goal geometry was associated with memory performance. 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