A fully polarizable implementation of the hybrid Quantum Mechanics/Molecular Mechanics approach is presented, where the classical environment is described through the AMOEBA polarizable force field. A variational formalism, offering a self-consistent 1 relaxation of both the MM induced dipoles and the QM electronic density is used for ground state energies and extended to electronic excitations in the framework of Time-Dependent Density Functional Theory combined with a state specific response of the classical part. An application to the calculation of the solvatochromism of the pyridinium N-phenolate betaine dye used to define the solvent ET30 scale is presented. The results show that the QM/AMOEBA model not only properly describes specific and bulk effects in the ground state but it also correctly responds to the large change in the solute electronic charge distribution upon excitation.