Scale-free neuronal dynamics and interareal correlations are emergent characteristics of spontaneous brain activity. How such dynamics and the anatomical patterns of neuronal connectivity are mutually related in brain networks has, however, remained unclear. We addressed this relationship by quantifying the network colocalization of scale-free neuronal activity—both neuronal avalanches and long-range temporal correlations (LRTCs)—and functional connectivity (FC) by means of intracranial and noninvasive human resting-state electrophysiological recordings. We found frequency-specific colocalization of scale-free dynamics and FC so that the interareal couplings of LRTCs and the propagation of neuronal avalanches were most pronounced in the predominant pathways of FC. Several control analyses and the frequency specificity of network colocalization showed that the results were not trivial by-products of either brain dynamics or our analysis approach. Crucially, scale-free neuronal dynamics and connectivity also had colocalized modular structures at multiple levels of network organization, suggesting that modules of FC would be endowed with partially independent dynamic states. These findings thus suggest that FC and scale-free dynamics—hence, putatively, neuronal criticality as well—coemerge in a hierarchically modular structure in which the modules are characterized by dense connectivity, avalanche propagation, and shared dynamic states. Author Summary The framework of criticality has been suggested to explain the scale-free dynamics of neuronal activity in complex interaction networks. However, the in vivo relationship between scale-free dynamics and functional connectivity (FC) has remained unclear. We used human intracranial and noninvasive electrophysiological measurements to map scale-free dynamics and connectivity. We found that the propagation of fast activity avalanches and the interareal coupling of slow, long-range temporal correlations—two key forms of scale-free neuronal dynamics—were nontrivially colocalized with the strongest functional connections. Most importantly, scale-free dynamics and FC exhibited similar modular network structures. FC and scale-free dynamics, and possibly also neuronal criticality, appear to co-emerge in a modular architecture in which the modules are characterized internally by shared dynamic states, avalanche propagation, and dense functional connectivity.