Already moderate alcohol consumption has detrimental long-term effects on brain function. However, how alcohol produces its potent addictive effects despite being a weak reinforcer is a poorly understood conundrum that likely hampers the development of successful interventions to limit heavy drinking. In this translational study, we demonstrate widespread increased mean diffusivity in the brain gray matter of chronically drinking humans and rats. These alterations appear soon after drinking initiation in rats, persist into early abstinence in both species, and are associated with a robust decrease in extracellular space tortuosity explained by a microglial reaction. Mathematical modeling of the diffusivity changes unveils an increased spatial reach of extrasynaptically released transmitters like dopamine that may contribute to alcohol’s progressively enhanced addictive potency.