FeO is a crucial component of the Earth's core, and its thermodynamic properties are essential to developing more accurate core models. It is also a notorious correlated insulator in the NaCl-type (B1) phase at ambient conditions. It undergoes two polymorphic transitions at 300 K before it becomes metallic in the NiAs-type (B8) structure at ~100 GPa. Although its phase diagram is not fully mapped, it is well established that the B8 phase transforms to the CsCl-type (B2) phase at core pressures and temperatures. Here, we report a successful ab initio calculation of the B8↔B2 phase boundary in FeO at Earth's core pressures. We show that fully anharmonic free energies computed with the Perdew-Burke-Ernzerhof-generalized gradient approximation coupled with thermal electronic excitations reproduce the experimental phase boundary within uncertainties at P > 255 GPa, including the largely negative Clapeyron slope of -52 MPa/K. This study validates the applicability of a standard density functional theory functional to FeO under Earth's core conditions and demonstrates the theoretical framework that enables complex predictive studies of this region.