Epidemiological research reveals that insufficient sleep in children has negative cognitive and emotional consequences; however, the physiological underpinnings of these observations remain understudied. We tested the hypothesis that the topographical distribution of deep sleep slow wave activity during the childhood predicts brain white matter microstructure (myelin) 3.5 y later. Healthy children underwent sleep high-density EEG at baseline (n = 13; ages 2.4–8.0 y) and follow-up (n = 14; ages 5.5–12.2 y). At follow-up, myelin (myelin water fraction) and cortical morphology were also quantified. Our investigation revealed 3 main findings. (1) The Frontal/Occipital (F/O)-ratio at baseline strongly predicted whole brain myelin at follow-up. (2) At follow-up, the F/O-ratio was only minimally (negatively) linked to brain myelin. (3) Cortical morphology was not related to the F/O-ratio, neither at baseline nor at follow-up. Our results support the hypothesis that during child development EEG markers during sleep longitudinally predict brain myelin content. Data extend previous findings reporting a link between EEG markers of sleep need and cortical morphology, by supporting the hypothesis that sleep is a necessary component to underlying processes of brain, and specifically myelin, maturation. In line with the overarching theory that sleep contributes to neurodevelopmental processes, it remains to be investigated whether chronic sleep loss negatively affects white matter myelin microstructure growth during sensitive periods of development.