The morphotropic phase boundary (MPB), which is the boundary separating a tetragonal phase from a rhombohedral phase by varying the composition or mechanical pressure in ferroelectrics, has been studied extensively for decades because it can lead to strong enhancement of piezoelectricity. Recently, a parallel ferromagnetic MPB was experimentally reported in the TbCo2-DyCo2 ferromagnetic system and this discovery proposes a new way to develop potential materials with giant magnetostriction. However, the role of magnetic domain switching and spin reorientation near the MPB region is still unclear. For the first time, we combine micromagnetic theory with Monte Carlo simulation to investigate the evolution of magnetic domain structures and the corresponding magnetization properties near the MPB region. It is demonstrated that the magnetic domain structure and the corresponding magnetization properties are determined by the interplay among anisotropy energy, magnetostatic energy and exchange energy. If the anisotropy energy barrier is large compared with the magnetostatic energy barrier and the exchange energy barrier, the MPB region is a T and R mixed structure and magnetic domain switching is the dominant mechanism. If the anisotropy energy barrier is small, the MPB region will also contain M phases and spin reorientation is the dominant mechanism. Our work could provide a guide for the design of advanced ferromagnetic materials with enhanced magnetostriction.