Iron nitrides are possible constituents of the cores of Earth and other terrestrial planets. Pressure‐induced magnetic changes in iron nitrides and effects on compressibility remain poorly understood. Here we report synchrotron X‐ray emission spectroscopy (XES) and X‐ray diffraction (XRD) results for ε‐Fe7N3 and γ’‐Fe4N up to 60 GPa at 300 K. The XES spectra reveal completion of high‐ to low‐spin transition in ε‐Fe7N3 and γ’‐Fe4N at 43 and 34 GPa, respectively. The completion of the spin transition induces stiffening in bulk modulus of ε‐Fe7N3 by 22% at ~40 GPa, but has no resolvable effect on the compression behavior of γ’‐Fe4N. Fitting pressure‐volume data to the Birch‐Murnaghan equation of state yields V0 = 83.29±0.03 (Å3), K0 = 232±9 GPa, K0’ = 4.1±0.5 for nonmagnetic ε‐Fe7N3 above the spin transition completion pressure, and V0 = 54.82±0.02 (Å3), K0 = 152±2 GPa, K0’ = 4.0±0.1 for γ’‐Fe4N over the studied pressure range. By re‐examining evidence for spin transition and effects on compressibility of other candidate components of terrestrial planet cores, Fe3S, Fe3P, Fe7C3, and Fe3C based on previous XES and XRD measurements, we located the completion of high‐ to low‐spin transition at ~67, 38, 50, and 30 GPa at 300 K, respectively. The completion of spin transitions of Fe3S, Fe3P and Fe3C induces elastic stiffening, whereas that of Fe7C3 induces elastic softening. Changes in compressibility at completion of spin transitions in iron‐light element alloys may influence the properties of Earth’s and planetary cores.