We characterize the europium (Eu3+) hyperfine interaction of the excited state (5D0) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under a weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian, we discuss the possibility to predict optical transition probabilities between hyperfine levels for the 7F0⟷5D0 transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of 151Eu3+:Y2SiO5 material under external magnetic fields.