Herein is presented a density functional theory (DFT) study of reactivity and structural properties of transition metal complexes of the Schiff base ligand 2,2'(1E,1'E)-(ethane-1,2-diylbis(azan-1-yl-1-ylidene))bis(phenylmethan-1-yl-1-ylidene)dibenzoic acid (hereafter denoted EDA2BB) with Cu(II), Mn(II), Ni(II), and Co(II). The quantum theory of atoms-in-molecules (QTAIM), conceptual DFT, natural population analysis (NPA), and molecular electrostatic potential (MEP) methods have been used. Results have revealed a distorted octahedral geometry around the central metal ion in each gas phase complex. In the DMSO solvent, a general axial elongation of metal-oxygen bonds involving ancillary water ligands has been observed, suggestive of loosely bound water molecules to the central metal ion that may be acting as solvent molecules. Weak, medium, and strong intramolecular hydrogen bonds along with hydrogen-hydrogen and van der Waals interactions have been elucidated in the complexes investigated via geometric and QTAIM analyses. From the chemical hardness values, the complex [Co(EDA2BB)(OH2)2] is the hardest, while [Cu(EDA2BB)(OH2)2] is the softest. Based on the global electrophilicity index, the complexes [Ni(EDA2BB)(OH2)2] and [Cu(EDA2BB)(OH2)2] are the strongest and weakest electrophiles, respectively, among the complexes studied. In conclusion, the reactivity of the complexes is improved vis-à-vis the ligand, and stable geometries of the complexes are identified, alongside their prominent electrophilic and nucleophilic sites.