Nine novel cobalt(III) ternary complexes bearing 4N donor ligands (tris(2-aminoethyl)amine (tren) or tris(2-methylpyridyl)amine (tpa)) and (fluoro)quinolones (quinH) with antibacterial and potential antitumor activity have been synthesized, characterized and screened in various biological assays. The molecular structures of [Co(tpa)(nal)](PF6)2 (3) and [Co(tpa)(nor)(Co(tpa)(norH)](PF6)3(Cl)2∙5MeOH (8) (nal = deprotonated form of nalidixic acid, norH = norfloxacin) with the expected octahedral geometry and (O,O) coordination of the quinolone ligands are also reported. Cyclic voltammetric studies revealed that the 4N donor ligands have much higher effect on the reduction potential of these ternary complexes than the quinolones. Due to the π-back-bonding interaction of the metal ion with the pyridyl-N atoms, the tpa containing compounds demonstrated lower stability and were easier to get reduced in a reversible manner. This character makes them unlikely candidates for development of effective, highly selective hypoxia-activated pro-drug complexes, but this goal might be achieved by substitution of tpa by tren. [Co(tren)(cip)](PF6)2 (4) and [Co(tpa)(cip)](PF6)2 (5) (cip = deprotonated form of ciprofloxacin) showed slightly less antibacterial activity against Escherichia coli than free ciprofloxacin (cipH) and they found to have very low toxicity towards both selected cancer (HeLa, MCF 7, MDA-MB-239) and noncancerous (MRC5 pd30) cells. Interaction of 4 and 5 with calf thymus DNA studied by UV-Vis, flow linear dichroism, viscometry and DNA melting indicated the complexes to bind to DNA as intercalators. DNA electrophoresis revealed that, unlike Co(II) complexes, 4 and 5 are not capable of cleaving DNA, but they can inhibit bacterial DNA gyrase 5 being slightly more active than 4.