The cellular maturational processes behind cognitive development during childhood, including the development of working memory capacity, are still unknown. By using the most standard computational model of visuospatial working memory, we investigated the consequences of cellular maturational processes, including myelination, synaptic strengthening, and synaptic pruning, on working memory-related brain activity and performance. We implemented five structural developmental changes occurring as a result of the cellular maturational processes in the biophysically based computational network model. The developmental changes in memory activity predicted from the simulations of the model were then compared to brain activity measured with functional magnetic resonance imaging in children and adults. We found that networks with stronger fronto-parietal synaptic connectivity between cells coding for similar stimuli, but not those with faster conduction, stronger connectivity within a region, or increased coding specificity, predict measured developmental increases in both working memory-related brain activity and in correlations of activity between regions. Stronger fronto-parietal synaptic connectivity between cells coding for similar stimuli was thus the only developmental process that accounted for the observed changes in brain activity associated with development of working memory during childhood.