First principles modeling is conducted to scrutinize the structural, chemical, electronic structures, bonding character, and magneto-optical features of intrinsic or pure anatase TiO2, Fe or Mn single-atom doped, and Mn–Fe diatom co-doped anatase TiO2 systems, respectively. Herein, the spin-polarized density functional theory (DFT) concerted with the on-site Hubbard (U) correction scheme for the Coulomb interaction, is utilized for the exchange-correlation term, as the generalized gradient approximation (GGA)+U. The spin-polarized density of states of Mn mono-atom doped anatase TiO2 material indicated a magnetic semiconductor attribute for both down/up spin components. Conversely, the outcome spin-polarized density of states of both Fe-doped and Mn–Fe co-doped anatase TiO2 materials illustrated the emergence of an intermediate band behavior. Accordingly, three magnetic impurity bands are produced in Mn–Fe co-doped anatase TiO2, the first two spin-up bands are located just uppermost the valence states nearby the Fermi level and the third spin-up/down band is lying far from the Fermi level just below the minimum conduction band. Interestingly, the spin-polarized charge density displayed an orbital ordering between the O 2p-orbitals and 3d-orbitals of Mn–Fe doped diatoms in the host TiO2 anatase system. The valuable optical ingredients, such as the optical absorption coefficient, refractive index, reflectivity spectra, optical conductivity, and electron energy loss function, are inspected and discussed. Moreover, the optical absorption coefficient characteristics of the mono-doped Mn/Fe and Mn–Fe co-doped TiO2 anatase structure displayed a relocation in the absorption feature edges towards the visible electromagnetic radiation regime. This means that the induced impurity bands delineate the essential contributor for boosting the catalytic activity in the visible light. It is expected that the Fe–Mn co-doped anatase TiO2 system could be a compelling candidate for its ultimate use in the photo-catalysts or magnetic storage devices.