The crystal structures and magnetic properties of seven kinds of [1,2,5]thiadiazolo[3,4-f][1,10]phenanthroline 1,1-dioxide (tdapO2) radical-anion salts, namely, K·tdapO2, K·tdapO2·0.5MeCN, K·(tdapO2)2, Rb·(tdapO2)2, Cs7·(tdapO2)6·ClO4, (NH4)2·tdapO2·I, and Hppda·tdapO2·MeCN, were investigated. Single-crystal X-ray analyses of these radical-anion salts revealed formation of π-stacking columns and the presence of intercolumnar coordination bonding or hydrogen bonding. The intermolecular magnetic coupling constants in these salts range from strong antiferromagnetic (J/kB = -310 K) to ferromagnetic (J/kB = 24 K). Ab initio calculations performed on the nearest-neighbor radical pairs in the π-stacking columns suggested that the magnetic interactions are strongly governed by the overlap between the two anionic radical species and well explain the observed ferromagnetic and antiferromagnetic interactions. In addition, calculations of a hypothetical oxygen-less tdap analogue suggested that the presence of oxygen in tdapO2 significantly reduces the hopping integral and enhances the probability of ferromagnetic interaction.