Fe-based amorphous and nanocrystalline soft magnetic alloys are regarded as the significant dual-green energy-saving materials because of their superior magnetic properties and straightforward fabrication procedure. As such, they have attracted much attention in the fields of the electronic information and electrical power. In this work, Fe_73.5Cu₁Nb₃Si_13.5B₉ (%) amorphous alloy ribbon is subjected to various physical ageing treatments in nitrogen atmosphere. These treatments include annealing at 540 ℃ for 30 min under different tensile stresses and isothermal tempering without tensile stress for several cycles. The origin of stress-induced magnetic anisotropy is investigated through using dynamic strain analysis, the longitudinally driven giant magento-impedance effect, and synchrotron radiation X-ray diffraction. In the process of tensile stress annealing, it is found that the axial strain of ribbon is elastic strain when annealing temperature is below the glass transition point, and plastic strain when annealing temperature is above the glass transition point; the precipitation of nanocrystalline phase has a pinning effect on amorphous matrix, which slows down the strain rates and makes the tend stable. Additionally, isothermal tempering studies show that the stress-induced magnetic anisotropy and lattice plane anisotropy have different relaxation patterns. It is found through numerical fitting that the stress-induced magnetic anisotropy can reach a stable value of 0.144 by infinite tempering, whereas the lattice plane anisotropy can only relax to zero by finite tempering. A model of nanocrystalline grain distribution anisotropy is developed to re-examine the origin of stress-induced magnetic anisotropy. It supports a viewpoint that the nanocrystalline grain distribution anisotropy \Delta \delta is responsible for the stress-induced irreversible magnetic anisotropy K_\textd, and that their relationship can be described as a following function: K_\textd = k\Delta \delta . Therefore, it is proposed that the stress-induced anisotropy originates from a synergistic interaction between the lattice plane anisotropy and the nanocrystalline grain distribution anisotropy in Fe-based alloy ribbon. This work has important implications for understanding the mechanism of the stress-induced magnetic anisotropy.