The synthesis and structural characterization of a series of supramolecular complexes of bicyclic cationic pyridine-fused 1,2,4-selenodiazoles with various anions is reported. The binding of trifluoroacetate, tetrachloroaurate, tetraphenylborate, perrhenate, and pertechnetate anions in the solid state is regarded. All the anions interact with selenodiazolium cations exclusively via a pair of “chelating” Se⋯O and H⋯O non-covalent interactions, which make them an attractive, novel, non-classical supramolecular recognition unit or a synthon. Trifluoroacetate salts were conveniently generated via novel oxidation reaction of 2,2′-dipyridyl diselenide with bis(trifluoroacetoxy)iodo)benzene in the presence of corresponding nitriles. Isolation and structural characterization of transient 2-pyridylselenyl trifluoroacetate was achieved. X-ray analysis has demonstrated that the latter forms dimers in the solid state featuring very short and strong Se⋯O and Se⋯N ChB contacts. 1,2,4-Selenodiazolium trifluoroacetates or halides show good solubility in water. In contrast, (AuCl4)−, (ReO4)−, or (TcO4)− derivatives immediately precipitate from aqueous solutions. Structural features of these supramolecular complexes in the solid state are discussed. The nature and energies of the non-covalent interactions in novel assembles were studied by the theoretical methods. To the best of our knowledge, this is the first study that regards perrhenate and pertechnetate as acceptors in ChB interactions. The results presented here will be useful for further developments in anion recognition and precipitation involving cationic 1,2,4-selenodiazoles.