A method is developed to calculate the ligand field (LF) parameters and the multiplet spectra of local magnetic centers with open d and f shells in solids in a parameter-free way. This method proceeds from density functional theory and employs Wannier projections of nonmagnetic band structures onto local d or f orbitals. Energies of multiplets and optical, as well as x-ray spectra are determined by exact numerical diagonalization of a local Hamiltonian describing Coulomb, LF, and spin-orbit interactions. The method is tested for several 3d and 5f compounds for which the LF parameters and multiplet spectra are experimentally well known. In this way, we obtain good agreement with the experiments for La2NiO4, CaCuO2, Li2CuO2, ZnO:Co, and UO2.