The recovery of a modulated magnetic structure in epitaxial BiFeO3 thin films as revealed by neutron diffraction is reported. The magnetic structure in thin films is found to strongly depend on substrate orientation. The substrate orientation causes different strain-relaxation processes resulting in different thin-film crystal structures. The (110) oriented film with a monoclinic structural phase has a single-domain modulated magnetic structure where the magnetic moment lies in the HHL plane. For the (111) oriented film that has a rhombohedral structure, a modulated structure superimposed on the G-type antiferromagnetic order is found. These results indicate that slight structural modifications in the BiFeO3 thin film cause drastic changes in the magnetic structure.