Globoid cell leukodystrophy (GLD) is an inherited lysosomal storage disease caused by β-galactocerebrosidase (GALC) deficiency. Gene therapy (GT) should provide rapid, extensive and lifetime GALC supply in central nervous system (CNS) tissues to prevent or halt irreversible neurologic progression. Here we used a lentiviral vector (LV) to transfer a functional GALC gene in the brain of Twitcher mice, a severe GLD model. A single injection of LV.GALC in the external capsule of Twitcher neonates resulted in robust transduction of neural cells with minimal and transient activation of inflammatory and immune response. Importantly, we documented a proficient transduction of proliferating and post-mitotic oligodendroglia, a relevant target cell type in GLD. GALC activity (30–50% of physiological levels) was restored in the whole CNS of treated mice as early as 8 days post-injection. The early and stable enzymatic supply ensured partial clearance of storage and reduction of psychosine levels, translating in amelioration of histopathology and enhanced lifespan. At 6 months post-injection in non-affected mice, LV genome persisted exclusively in the injected region, where transduced cells overexpressed GALC. Integration site analysis in transduced brain tissues showed no aberrant clonal expansion and preferential targeting of neural-specific genes. This study establishes neonatal LV-mediated intracerebral GT as a rapid, effective and safe therapeutic intervention to correct CNS pathology in GLD and provides a strong rationale for its application in this and similar leukodystrophies, alone or in combination with therapies targeting the somatic pathology, with the final aim of providing an effective and timely treatment of these global disorders.