From Co(NO3)2·6H2O ‐ NaN3 ‐ abpt reaction system, a mononuclear complex [Co(abpt)2(N3)2] (abpt = 4‐amino‐3,5‐bis(pyridin‐2‐yl)‐1,2,4‐triazole) (1) and a dinuclear complex [Co2(abpt)(µ‐abpt‐H)2(N3)4]·1.12H2O (2) were obtained. The presence of neutral abpt, as well as azido ligands was proved by IR spectroscopy. X‐ray crystallography shows that 1 is a molecular CoII complex with two azido ligands coordinated in trans‐positions, while 2 is a dinuclear CoIII complex bridged by two abpt‐H ligands. π–π stacking interactions between pyridyl rings of abpt and N‐H···N and C‐H···N hydrogen bonds in 1 and 2 stabilize their structures by creating a 3D supramolecular network. The analysis of the magnetic properties of 1 revealed negative zero‐field splitting parameter D = –24.1 cm–1 supported also by CASSCF/NEVPT2 and CASSCF/CASPT2 theoretical calculations. The X‐band electron paramagnetic resonance also gives an evidence for a strong rhombic character of the anisotropy. The investigation of the ac susceptibility measurements identified 1 as a field‐induced single‐molecule magnet, in which direct, Raman and Orbach relaxation processes are present.