In the framework of the stochastic approach to the description of the interaction between the quantum dimer nanocluster with two electrons and dissipative environment, such as a weak structured organic matrix, the electron transfer kinetics is theoretically investigated. The minimal theoretical model formulated here involves the applying of Redfield's theory for the reduced density matrix and the using of Haken-Strobl approximation. The dimer nanocluster is considered in the model "two centers - two electrons", which is described with using of Hubbard's Hamiltonian, so that the electron correlation is taken into account. It was found that the difference in the electron populations on the dimer nanocluster centers has an oscillatory time dependence with a beats, which is damping due to the influence of a weak structured matrix as a thermostat. This manifests itself as a change in the nanodimer dipole moment, i.e. during of the relaxation time determined by a dissipative environment holds the switching of nanodimer between the states with the opposite directions of its dipole moment. Eventually, the dimer nanocluster relaxes from an initial state with two electrons on one center to the final state with a uniform distribution of electrons on the centers. It is shown how the switching is modified for the different values of the nanodimer parameters and dissipation parameter. This switching regime in the nanosystem studied here is interesting for various device applications due to the ability to control the state of such nanosystem by action of the external electric and magnetic fields.