Neural oscillations subserve many human perceptual and cognitive operations. Accordingly, brain functional connectivity is not static in time, but fluctuates dynamically following the synchronization and desynchronization of neural populations. This dynamic functional connectivity has recently been demonstrated in spontaneous fluctuations of the Blood Oxygen Level-Dependent (BOLD) signal, measured with functional Magnetic Resonance Imaging (fMRI). We analyzed temporal fluctuations in BOLD connectivity and their electrophysiological correlates, by means of long (≈ 50 min) joint electroencephalographic (EEG) and fMRI recordings obtained from two populations: 15 awake subjects and 13 subjects undergoing vigilance transitions. We identified positive and negative correlations between EEG spectral power (extracted from electrodes covering different scalp regions) and fMRI BOLD connectivity in a network of 90 cortical and subcortical regions (with millimeter spatial resolution). In particular, increased alpha (8-12 Hz) and beta (15-30 Hz) power were related to decreased functional connectivity, whereas gamma (30-60 Hz) power correlated positively with BOLD connectivity between specific brain regions. These patterns were altered for subjects undergoing vigilance changes, with slower oscillations being correlated with functional connectivity increases. Dynamic BOLD functional connectivity was reflected in the fluctuations of graph theoretical indices of network structure, with changes in frontal and central alpha power correlating with average path length. Our results strongly suggest that fluctuations of BOLD functional connectivity have a neuro-physiological origin. Positive correlations with gamma can be interpreted as facilitating increased BOLD connectivity needed to integrate brain regions for cognitive performance. Negative correlations with alpha suggest a temporary functional weakening of local and long-range connectivity, associated with an idling state.