Background: White matter hyperintensity (WMH) is a hallmark of cerebral small vessel disease and an important contributor to vascular cognitive impairment (VCI), yet lesion burden incompletely explains interindividual variability in cognitive outcomes across the VCI continuum. Functional connectome signatures relevant to this variability remain incompletely characterized. Methods: We analyzed multicenter resting-state functional MRI data from 247 participants spanning vascular risk factors with normal cognition, vascular mild cognitive impairment, and vascular dementia. Exploratory external testing was performed in an independent dataset of 37 participants. Connectome-based predictive modeling (CPM) with permutation testing was used. To reduce circularity, we computed cross-validated network strength (cvNS) using predictive masks defined within training folds only. Results: We identified cross-validated functional connectivity patterns associated with MoCA (positive model, p_perm = 0.034) and TMT-B performance (negative model, p_perm = 0.001). These patterns were most prominently represented in Frontoparietal, Motor, and Subcortical–Cerebellar regions. The TMT-B negative network showed a substantial contribution from weak between-network connections (64.4% of predictive edges). In the external dataset, network strength computed from discovery consensus masks remained associated with MoCA. Greater WMH volume was associated with worse TMT-B performance, and mediation analyses indicated that cvNS computed from the TMT-B connectivity pattern statistically linked WMH volume to both TMT-B (indirect = 0.090, 95% CI [0.018, 0.225], p = 0.023) and MoCA performance (indirect = −0.007, 95% CI [−0.019, −0.001], p = 0.031). Conclusions: CPM-derived functional connectivity patterns capture meaningful continuous variability in cognition across the VCI continuum and provide statistical support consistent with WMH-related functional disconnection as a network-level correlate of cognitive impairment.