Exchange-coupled BiFeO3/ferromagnet thin film heterostructures are promising for a fast and power efficient control of magnetization of the ferromagnetic layer. In the paper, the results of the study of magnetic properties of the epitaxial Fe2B/BiFeO3 heterostructure on (001)-SrTiO3 substrate with ferromagnetic resonance (FMR) spectroscopy are presented. The hierarchy of magnetic anisotropies that determine the angular variation of the resonance field in-plane and in-/out-of the plane of the system include the tetragonal four-fold and uniaxial terms for the Fe2B layer, uniaxial term for antiferromagnetic BiFeO3 layer and the exchange coupling at the interface. We find out that the exchange bias direction can be switched by a strong enough applied magnetic field. Both the exchange bias and an in-plane FMR resonance field of the heterostructure are strongly affected by the illumination with k = 405 nm light. An optical tunability of the exchange bias and ferromagnetic resonance fields of the heterostructure has been demonstrated.