A theoretical investigation is presented on the properties of charge transfer excitons at vertically coupled semiconductor quantum dots in the presence of electric and magnetic fields directed along the growth axis. Such excitons should have two interesting characteristics: an extremely long lifetime and a permanent dipole moment. We show that wave functions and the low-lying energies of charge transfer exciton can be found exactly for a special morphology of quantum dots that provides a parabolic confinement inside the layers. To take into account a difference between confinement potentials of an actual structure and of our exactly solvable model, we use the Galerkin method. The density of energy states is calculated for different InAs/GaAs quantum dots' dimensions, the separation between layers, and the strength of the electric and magnetic fields. A possibility of a formation of a giant dipolar momentum under external electric field is predicted.