Recent experimental studies have shown that early brain activity is crucial for neuronal survival and the development of brain networks; however, it has been challenging to assess its role in the developing human brain. We employed serial quantitative magnetic resonance imaging to measure the rate of growth in circumscribed brain tissues from preterm to term age, and compared it with measures of electroencephalographic (EEG) activity during the first postnatal days by 2 different methods. EEG metrics of functional activity were computed: EEG signal peak-to-peak amplitude and the occurrence of developmentally important spontaneous activity transients (SATs). We found that an increased brain activity in the first postnatal days correlates with a faster growth of brain structures during subsequent months until term age. Total brain volume, and in particular subcortical gray matter volume, grew faster in babies with less cortical electrical quiescence and with more SAT events. The present findings are compatible with the idea that (1) early cortical network activity is important for brain growth, and that (2) objective measures may be devised to follow early human brain activity in a biologically reasoned way in future research as well as during intensive care treatment.