The magnetic structure and susceptibilities of Fe₂SiO₄ were derived on the basis of localized magnetic moments. Each Fe²⁺ ion is described as a ⁵D state, and crystal field, spin-orbit coupling, isotropic Heisenberg exchange, magnetic dipole-dipole interaction and external magnetic fields are taken into account. Many-particle interactions are treated in the mean-field approximation. Fundamental physical constants such as crystal-field splittings and exchange integrals are fitted to reproduce experimental results. Within this model very good agreement between theory and experiment was obtained. It is shown that the canting of magnetic moments at inversion centres is a consequence of competition between the crystal field and strong antiferromagnetic coupling to the moments in mirror planes, each preferring different orientations. The ratio of these effects is temperature dependent and explains the evolution of the canting angle. Further high-field magnetizations are determined and with the field in the (010) direction a field-induced phase transition and the magnetic phase diagram are predicted. The temperature dependence of quadrupole splitting in Mossbauer experiments is also calculated and compared with experimental results.