Pyrazolate‐based dinucleating ligands with thioether‐containing chelate arms have been used for the synthesis of a family of novel tetranuclear nickel(II) complexes [L2Ni4(N3)3(O2CR)](ClO4)2 that incorporate three azido bridges and one carboxylate (R = Me, Ph). Molecular structures have been elucidated by X‐ray crystallography in four cases, revealing Ni4 cores with a unique topology in which two of the azido ligands adopt an unusual μ3‐1,1,3 bridging mode. The compounds were further characterized by mass spectrometry, IR spectroscopy, and variable‐temperature magnetic susceptibility measurements. Magnetic data analyses indicate a combination of significant intramolecular ferromagnetic and antiferromagnetic exchange interactions that give rise to an overall ST = 0 ground state. The sign and the magnitude of the individual couplings have been rationalized in the framework of the common magnetostructural correlations for end‐to‐end and end‐on azido linkages, suggesting that these correlations also remain valid for the respective fragments of multiply bridging μ3‐1,1,3 azido ligands.