Human neuronal circuits undergo life-long functional reorganization with profound effects on cognition and behavior. Well documented prolonged development of anatomical brain structures includes white and gray matter changes that continue into the third decade of life. We investigated resting-state EEG oscillations in 1433 subjects from 5 to 71 years. Neuronal oscillations exhibit scale-free amplitude modulation as reflected in power-law decay of autocorrelations--also known as long-range temporal correlations (LRTC)--which was assessed by detrended fluctuation analysis. We observed pronounced increases in LRTC from childhood to adolescence, during adolescence, and even into early adulthood (∼25 years of age) after which the temporal structure stabilized. A principal component analysis of the spatial distribution of LRTC revealed increasingly uniform scores across the scalp. Together, these findings indicate that the scale-free modulation of resting-state oscillations reflects brain maturation, and suggests that scaling analysis may prove useful as a biomarker of pathophysiology in neurodevelopmental disorders such as attention deficit hyperactivity disorder and schizophrenia.