We apply the Lang−Firsov (LF) transformation to electron−boson coupled Hamiltonians and variationally optimize the transformation parameters and molecular orbital coefficients to determine the ground state. Møller−Plesset (MP-n, with n = 2 and 4) perturbation theory is then applied on top of the optimized LF mean-field state to improve the description of electron−electron and electron−boson correlations. The method (LF−MP) is applied to several electron−boson coupled systems, including the Hubbard−Holstein model, diatomic molecule dissociation (H 2 , HF), and the modification of proton transfer reactions (malonaldehyde and aminopropenal) via the formation of polaritons in an optical cavity. We show that with a correction for the electron−electron correlation, the method gives quantitatively accurate energies comparable to that by exact diagonalization or coupled-cluster theory. The effects of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed.