[en] The single-site two-electron exchange amplitude J_sd between the Cu 4s and Cu 3d_x²-y² states is found to be the pairing mechanism of high-T_c overdoped cuprates. The noninteracting part of the Hamiltonian spans the copper Cu 4s, Cu 3d_x²-y² and oxygen O 2p_x and O 2p_y states. Within the standard BCS treatment an explicit expression for the momentum dependence of the gap Δ_p is derived and shown to fit the angle-resolved photoemission spectroscopy data. The basic thermodynamic and electrodynamic properties of the model (specific heat C(T) and London penetration depth λ(T)) are analytically derived. These are directly applicable to cuprates without complicating structural accessories (chains, double CuO₂ planes etc). We advocate that the pairing mechanism of overdoped and underdoped cuprates is the same, as T_c displays smooth doping dependence. Thus, a long-standing puzzle in physics is possibly solved