Magnetization states of amorphous soft ferromagnetic microwires are studied by experiment and theoretically. It is shown that in low applied axial fields, on increasing the circular magnetic field produced by current, the initial homogeneous circular magnetization distribution evolves in three sequential steps: (i) the appearance of a helical magnetization state, (ii) a jump to the helical state with opposite chirality, and (iii) a gradual rotation of magnetization toward the new circular state. An applied, large-enough axial field stabilizes the axial magnetization states, making these transitions continuous and shifting the magnetic hysteresis loops. The origin of these successive magnetization reorientations and switching is explained in the frameworks of the proposed model.