Over past decades, Fe-based amorphous and nanocrystalline alloys have aroused a popular research interest because of their ability to achieve high saturation magnetic flux density and low coercivity, but the mechanisms for modifying annealing-induced magnetic properties on an atomic scale in amorphous matrix due to structural relaxation has not been enough understood. In this work, we study the effects of pre-annealing time on local structural and magnetic properties of Fe80.8B10P8Cu1.2 amorphous alloy to explore the mechanisms for structural relaxation, particularly the evolution of chemical short range order. The alloy ribbons, both melt spun and annealed, are characterized by differential scanning calorimetry, X-ray diffractometry, Mössbauer spectroscopy and magnetometry. The magnetic hyperfine field distribution of Mössbauer spectrum is decomposed into four components adopting Gaussian distributions which represent FeB-, Fe3P-, Fe3B- and α-Fe-like atomic arrangements, respectively. The fluctuation of magnetic hyperfine field distribution indicates that accompanied with the aggregation of Fe atoms, the amorphous structures in some atomic regions tend to transform from Fe3B- to FeB-like chemical short-range order with the pre-annealing time increasing, but the amorphous matrix begins to crystallize when the pre-annealing time reaches 25 min. Before crystallization, the spin-exchange interaction between magnetic atoms is strengthened due to the increase of the number of Fe clusters and the structure compaction. Thus, saturation magnetic flux density increases gradually, then shows a drastic rise when there appear α-Fe grains in the amorphous matrix. Coercivity first declines to a minimum after 5 min pre-annealing and then increases drastically. This is attributed to the fact that excess free volume and residual stresses in the melt spun sample are released out during previous pre-annealing, which can weaken magnetic anisotropy significantly, while the subsequent pre-annealing destroys the homogeneity of amorphous matrix, resulting in the increase of magnetic anisotropy. In addition, the separation of Cu atoms from the first near-neighbor shell of Fe atoms and the obvious decrease in the Fe-P coordination number suggest the formation of CuP clusters, which can provide heterogeneous nucleation sites for α-Fe and contribute to the grain refinement. Therefore, through controlling the pre-annealing time, we successfully tune the content values of CuP and Fe clusters in the amorphous matrix to promote the precipitation of α-Fe and refine grains during crystallization. For Fe80.8B10P8Cu1.2 nanocrystalline alloy, an enhancement of soft magnetic properties is achieved by a pre-annealing at 660 K for 5-10 min followed by a subsequent annealing at 750 K for 5 min.