In this joint experimental and ab initio study, we focused on the influence of the chemical composition and martensite phase transition on the electronic, magnetic, optical, and magneto-optical properties of the ferromagnetic shape-memory Ni-Mn-Ga alloys. The polar magneto-optical Kerr effect (MOKE) spectra for the polycrystalline sample of the Ni-Mn-Ga alloy of Ni₆₀Mn₁₃Ga₂₇ composition were measured by means of the polarization modulation method over the photon energy range 0.8 ≤ hν ≤ 5.8 eV in magnetic field up to 1.5 T. The optical properties (refractive index n and extinction coefficient k) were measured directly by spectroscopic ellipsometry using the rotating analyzer method. To complement experiments, extensive first-principles calculations were made with two different first-principles approaches combining the advantages of a multiple scattering Green function method and a spin-polarized fully relativistic linear-muffin-tin-orbital method. The electronic, magnetic, and MO properties of Ni-Mn-Ga Heusler alloys were investigated for the cubic austenitic and modulated 7M-like incommensurate martensitic phases in the stoichiometric and off-stoichiometric compositions. The optical and MOKE properties of Ni-Mn-Ga systems are very sensitive to the deviation from the stoichiometry. It was shown that the ab initio calculations reproduce well experimental spectra and allow us to explain the microscopic origin of the Ni₂MnGa optical and magneto-optical response in terms of interband transitions. The band-by-band decomposition of the Ni₂MnGa MOKE spectra is presented and the interband transitions responsible for the prominent structures in the spectra are identified.