BaFe₂(PO₄)₂ was recently prepared by hydrothermal synthesis and identified as the first two-dimensional (2D) Ising ferromagnetic oxide, in which honeycomb layers made up of edge-sharing FeO₆ octahedra containing high-spin Fe²⁺ ions (S = 2) are isolated by PO₄ groups and Ba²⁺ cations. BaFe₂(PO₄)₂ has a trigonal R-3 structure at room temperature but adopts a triclinic P-1 structure below 140 K due to the Jahn-Teller (JT) instability arising from the (t_2g)⁴(e_g)² configuration. The triclinic crystal structure was refined to find significantly distorted Fe²⁺O₆ octahedra in the honeycomb layers while the distortion amplitude Q_JT was estimated to 0.019 Å. The JT stabilization energy is estimated to be 7 meV per formula unit by DFT calculations. Below 70 K, very close to the ferromagnetic transition temperature T_c = 65.5 K, the structure of BaFe₂(PO₄)₂ returns to a trigonal R-3 structure in the presence of significant ferromagnetic domains. This rare re-entrant structural transition is accompanied by a discontinuous change in the quadrupolar splitting of Fe²⁺, as determined by Mössbauer spectroscopy. EPR measurements show the presence of magnetic domains well above T_c , as expected for a ferromagnetic 2D Ising system, and support that the magnetism of BaFe₂(PO₄)₂ is uniaxial (g_⊥ = 0).