Non-invasive electrophysiology lacks methods that accurately reconstruct whole-brain spatiotemporal dynamics while incorporating individual cortical geometry, leaving current electroencephalography and magnetoencephalography source imaging limited by simplistic or biologically implausible priors. Here, we show that embedding participant-specific Geometric Basis Functions (GBFs), eigenmodes derived from each individual's cortical surface, provides a powerful anatomic constraint that resolves the inverse problem and improves reconstruction fidelity. The method reconstructs neural sources as linear combinations of geometric basis functions, thereby aligning source estimates with the geometric organization of neural dynamics. We validate GBF across the Meta-Source Benchmark, task-evoked data, resting-state networks, intracranial stimulation, and epilepsy data. The results demonstrate that GBF yields high localization accuracy and captures fast spatiotemporal dynamics consistent with anatomical pathways. These findings suggest that both spontaneous and evoked whole-brain activity can be described by hundreds of geometric modes, providing a compact yet accurate representation of neural sources. By linking cortical geometry to electrophysiological dynamics, GBF offers a versatile source imaging tool for both scientific and clinical applications.