The maturation of the cortical gray matter (GM) and white matter (WM) are described as sequential processes following multiple, but distinct rules. However, neither the mechanisms driving brain maturation processes, nor the relationship between GM and WM maturation are well understood. Here we use connectomics and two MRI measures reflecting maturation related changes in cerebral microstructure, namely the Apparent Diffusion Coefficient (ADC) and the T1 relaxation time (T1), to study brain development. We report that the advancement of GM and WM maturation are inter-related and depend on the underlying brain connectivity architecture. Particularly, GM regions and their incident WM connections show corresponding maturation levels, which is also observed for GM regions connected through a WM tract. Based on these observations, we propose a simple computational model supporting a key role for the connectome in propagating maturation signals sequentially from external stimuli, through primary sensory structures to higher order functional cortices.