The local structures and the g factors gi (i = x, y, z) for Ni3+ centers in Na2Zn(SO4)2·4H2O (DPPH) and K2Zn(SO4)2·6H2O (PHZS) crystals are theoretically studied by using the perturbation formulas of the g factors for a 3d7 ion with low spin (S = 1/2) in orthorhombically compressed octahedra. In these formulas, the contributions to g factors from both the spin‐orbit coupling interactions of the central ion and ligands are taken into account, and the required crystal‐field parameters are estimated from the superposition model and the local geometry of the systems. Based on the calculations, the Ni‐O bonds are found to suffer the axial compression δz (or Δz) of about 0.111 Å (or 0.036 Å) along the z‐axis for Ni3+ centers in DPPH (or PHZS) crystals. Meanwhile, the Ni‐O bonds may experience additional planar bond length variation δx (≈0.015 Å) along x‐ and y‐axes for the orthorhombic Ni3+ center in DPPH. The theoretical g factors agree well with the experimental data. The obtained local structural parameters for both Ni3+ centers are discussed.