Sr4Ru3O10, the n = 3 member of the Ruddlesden-Popper type ruthenate Sr n+1Ru n O3n+1, is known to exhibit a peculiar metamagnetic transition in an in-plane magnetic field. However, the nature of both the temperature- and field-dependent phase transitions remains as a topic of debate. Here, we have investigated the magnetic transitions of Sr4Ru3O10 via single-crystal neutron diffraction measurements. At zero field, we find that the system undergoes a ferromagnetic transition with both in-plane and out-of-plane magnetic components at T c \ 100 K. Below T - = 50 K, the magnetic moments incline continuously toward the out-of-plane direction. At T = 1.5 K, where the spins are nearly aligned along the c axis, a spin reorientation occurs above a critical field B c, giving rise to a spin component perpendicular to the plane defined by the field direction and the c axis. We suggest that both the temperature- and field-driven spin reorientations are associated with a change in the magnetocrystalline anisotropy, which is strongly coupled to the lattice degrees of freedom. This study elucidates the long-standing puzzles on the zero-field magnetic orders of Sr4Ru3O10 and provides new insights into the nature of the field-induced metamagnetic transition. \ 2018 The Author(s).