In response to a need of establishing a high-resolution spatiotemporal neuroimaging technology, tremendous efforts have been directed upon developing multimodal neuroimaging strategies that combine the complementary advantages of high-spatial-resolution functional magnetic resonance imaging (fMRI) and high-temporal-resolution electroencephalography (EEG) or magnetoencephalography (MEG). A critical challenge to the fMRI-EEG/MEG integration lies in the spatial mismatches between fMRI activations and instantaneous electrical source activities. Such mismatches are fundamentally due to the fact that fMRI and EEG/MEG signals are generated and collected in highly different time scales. In this paper, we propose a new theoretical framework to solve the problem of fMRI-EEG integrated cortical source imaging. The new framework has two principal technical advancements. First, by assuming a linear neurovascular coupling, a method is rigorously derived to quantify the fMRI signal in each voxel as proportional to the time integral of the power of local electrical current source over the period of event related potentials (ERP). Second, the EEG inverse problem is solved for every time instant using an adaptive Wiener filter, in which the prior time-variant source covariance matrix is estimated by combining the quantified fMRI responses and the segmented EEG signals before response averaging. Our preliminary computer simulation results suggest that the proposed method provides a reliable technique for the fMRI-EEG integration and represents a significant advancement over the conventional fMRI-weighted EEG (or MEG) source imaging techniques, and is also applicable to fMRI-MEG integrated source imaging.