COVID-19 vaccines already in use or in clinical development may have safety concerns, limited immunogenicity in high-risk groups or reduced efficacy against emerging SARS-CoV-2 variants. In addition, although the neurotropism of SARS-CoV-2 is well established, the vaccine strategies currently developed have not taken into account the protection of the central nervous system. Here, we generated a transgenic mouse strain expressing the human Angiotensin Converting Enzyme 2, with unprecedented brain as well as lung permissibility to SARS-CoV-2 replication. Using this stringent transgenic model, we demonstrated that a non-integrative lentiviral vector, encoding for the spike glycoprotein of the ancestral Wuhan SARS-CoV-2, used in intramuscular prime and intranasal boost elicits sterilizing protection of lung and brain against both the Wuhan and the most genetically distant Manaus P.1 SARS-CoV-2 variants. Beyond the induction of strong neutralizing antibodies, the mechanism underlying this broad protection spectrum involves a robust protective spike-specific CD8+ T-cell immunity, unaffected by the recent mutations accumulated in the emerging SARS-CoV-2 variants.