The novel polarizable FQFμ force field is proposed and coupled to a quantum mechanical (QM) SCF Hamiltonian. The peculiarity of the resulting QM/FQFμ approach stands in the fact the polarization effects are modeled in terms of both fluctuating charges and dipoles, which vary as a response to the external electric field/potential. Remarkably, QM/FQFμ is defined in terms of three parameters: electronegativity and chemical hardness, which are well-defined in density functional theory, and polarizability, which is physically observable. Such parameters are numerically adjusted to reproduce full QM reference electrostatic energy values. The model is challenged against test molecular systems in aqueous solution, showing remarkable accuracy and thus highlighting its potentialities for future extensive applications.