For the first time, in this study with the use of QM/QTAIM methods we have exhaustively investigated the tautomerization of the biologically-important conformers of the G*·C* DNA base pair—reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H), and reverse Hoogsteen G*′·C*(rH) DNA base pairs—via the single (SPT) or double (DPT) proton transfer along the neighboring intermolecular H-bonds. These tautomeric reactions finally lead to the formation of the novel G·CO2*(rWC), GN2*·C(rWC), G*′N2·C(rWC), GN7*·C(H), and G*′N7·C(rH) DNA base mispairs. Gibbs free energies of activation for these reactions are within the range 3.64–31.65 kcal·mol−1 in vacuum under normal conditions. All TSs are planar structures (Cs symmetry) with a single exception—the essentially non-planar transition state TSG*·C*(rWC)↔G+·C−(rWC) (C1 symmetry). Analysis of the kinetic parameters of the considered tautomerization reactions indicates that in reality only the reverse Hoogsteen G*′·C*(rH) base pair undergoes tautomerization. However, the population of its tautomerised state G*′N7·C(rH) amounts to an insignificant value−2.3·10−17. So, the G*·C*(rWC), G*′·C*(H), and G*′·C*(rH) base pairs possess a permanent tautomeric status, which does not depend on proton mobility along the neighboring H-bonds. The investigated tautomerization processes were analyzed in details by applying the author's unique methodology—sweeps of the main physical and chemical parameters along the intrinsic reaction coordinate (IRC). In general, the obtained data demonstrate the tautomeric mobility and diversity of the G*·C* DNA base pair.