Spontaneous (or resting-state) brain activity has attracted a growing body of neuroimaging research over the last decades. Whole-brain network models have proved helpful to investigate the source of slow (<0.1Hz) correlated hemodynamic fluctuations revealed in fMRI during rest. However, the mechanisms mediating resting-state long-distance correlations and the relationship with the faster neural activity remain unclear. Novel insights coming from MEG studies have shown that the amplitude envelopes of alpha- and beta-frequency oscillations (~8–30Hz) display similar correlation patterns as the fMRI signals.In this work, we combine experimental and theoretical work to investigate the mechanisms of spontaneous MEG functional connectivity. Using a simple model of coupled oscillators adapted to incorporate realistic whole-brain connectivity and conduction delays, we explore how slow and structured amplitude envelopes of band-pass filtered signals – fairly reproducing MEG data collected from 10 healthy subjects at rest – are generated spontaneously in the space-time structure of the brain network.Our simulation results show that the large-scale neuroanatomical connectivity provides an optimal network structure to support a regime with metastable synchronization. In this regime, different subsystems may temporarily synchronize at reduced collective frequencies (falling in the 8–30Hz range due to the delays) while the global system never fully synchronizes. This mechanism modulates the frequency of the oscillators on a slow time-scale (<0.1Hz) leading to structured amplitude fluctuations of band-pass filtered signals. Taken overall, our results reveal that the structured amplitude envelope fluctuations observed in resting-state MEG data may originate from spontaneous synchronization mechanisms naturally occurring in the space-time structure of the brain.