In many tokamaks ferromagnetic material, usually referred to as an iron-core, is present in order to improve the magnetic coupling between the solenoid and the plasma. The presence of the iron core in proximity to the plasma changes the magnetic topology with consequent eects on the magnetic field structure and the plasma boundary. This paper considers the problem of obtaining the free-boundary plasma equilibrium solution in the presence of ferromagnetic material based on measured constraints. The current approach employs a model described by O’Brien et al. in which the magnetization currents at the air-iron boundary are represented by a set of free parameters and appropriate boundary conditions are enforced via a set of quasi-measurements on the material boundary. This can lead to the possibility of overfitting the data and hiding underlying issues with the measured signals. Although the model typically achieves good fits to measured magnetic signals there are significant discrepancies in the inferred magnetic topology compared with other plasma diagnostic measurements that are independent of the magnetic field. An alternative approach for equilibrium reconstruction in iron-core tokamaks, termed the deterministic magnetisation model is developed and implemented in EFIT++. The iron is represented by a boundary current with the gradients in the magnetisation dipole state generating macroscopic internal magnetisation currents. A model for the boundary magnetisation currents at the iron-air interface is developed using B-Splines enabling continuity to arbitrary order; internal magnetisation currents are allocated to triangulated regions within the iron, and a method to enable adaptive refinement is implemented. The deterministic model has been validated by comparing it with a synthetic 2-D electromagnetic model of JET. It is established that the maximum field discrepancy is less than 1.5mT throughout the vacuum region enclosing the plasma. The discrepancies of simulated magnetic probe signals are accurate to within 1% for signals with absolute magnitude greater than 100mT; in all other cases agreement is to within 1mT. The eect of neglecting the internal magnetisation currents increases the maximum discrepancy in the vacuum region to >20mT, resulting in errors of 5-10% in the simulated probe signals. The fact that the previous model neglects the internal magnetisation currents (and also has additional free parameters when fitting the measured data) makes it unsuitable for analysing data in the absence of plasma current. The discrepancy of the poloidal magnetic flux within the vacuum vessel is to within 0.1Wb. Finally the deterministic model is applied to an equilibrium force-balance solution of a JET discharge using experimental data. It is shown that the discrepancies of the outboard separatrix position, and the outer strike-point position inferred from Thomson Scattering and Infrared camera data are much improved beyond the routine equilibrium reconstruction, whereas the discrepancy of the inner strike-point position is similar.