The structural parameters, spin states, quadrupole or dipole moments, embedding energies, and IR spectra of endohedral I−@C60, I−@C60+, I–@C58B2, I−@[C58B2]+, I−@[C59B]+, I−@[C60I]+, (I−@C60+)2, Te@C60, Te@C58B2, Xe@C60, and Xe@C58B2 complexes are predicted by quantum chemical DFT (U)PBE0 method. The nucleus of an endo-atom is localized in the vicinity of cage center. The distortion of the fullerene structure by the endo-atom is small. The electrically neutral complexes are metastable. The energies of I−@C60 and I−@C58B2 anions are lower than the sum of the energies of free components. The addition of the iodine exo-atom to the I−@C60+ free radical transforms it into the stable singlet I−@[C60I]+ zwitter-ion, the energy of which is lower than the energy of the molecule C60I2. The relaxation effect after β− decay of the radioiodide endo-anion in the fullerene cage is very small. The possibilities of synthesis of fullerene and heterofullerene endohedral complexes with radioactive iodine from a tellurium-containing precursor are discussed.