Abstract COVID‐19 vaccines already in use or in clinical development may have 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 protection of the central nervous system. Here, we generated a transgenic mouse strain expressing the human angiotensin‐converting enzyme 2, and displaying unprecedented brain permissiveness to SARS‐CoV‐2 replication, in addition to high permissiveness levels in the lung. Using this stringent transgenic model, we demonstrated that a non‐integrative lentiviral vector, encoding for the spike glycoprotein of the ancestral SARS‐CoV‐2, used in intramuscular prime and intranasal boost elicits sterilizing protection of lung and brain against both the ancestral virus, and the Gamma (P.1) variant of concern, which carries multiple vaccine escape mutations. Beyond induction of strong neutralizing antibodies, the mechanism underlying this broad protection spectrum involves a robust protective T‐cell immunity, unaffected by the recent mutations accumulated in the emerging SARS‐CoV‐2 variants.