Fe-based amorphous alloys are well known for their excellent soft magnetic and mechanical properties such as high saturation magnetization (B_s), very low coercive force (H_c), high magnetic permeability (μ), low core loss, and high strength, and they are suitable for application as transformer-core materials and have potential applications as structural materials. The minor addition of early transition metal (ETM) such as Zr, Nb, Mo, Hf, Ta, or W can effectively improve the glass-forming abilities, thermal stability, soft magnetic and mechanical properties of Fe-based metallic glasses. The beneficial effects of the minor addition on the glass-forming ability can generally be classified into three aspects: (1) it favors the formation of the unique atomic dense configurations with small free volumes, strong liquid behavior, and high viscosity, which are significantly different from those for conventional metallic glasses; (2) it makes the melts energetically closer to the crystalline state than other metallic melts due to their high packing density in conjunction with a tendency to develop short-range order; (3) it makes the melts more viscous, which leads to slow crystallization kinetics. Despite these advantages, the fundamental theory about the mechanism of the minor addition of ETM in glass formation and properties tailoring is yet to be fully established. In this study, a "cluster plus glue atom" local structure model has been proposed to explore the local structure-property correlation of metallic glasses. The accessibility of calorimetric glass transition (T_g), glass-forming ability, thermal glass stability, and the mechanical properties of metallic glasses are explained in terms of the intra- and inter-atomic cluster correlations in the amorphous structures. Based on the local structure model, the T_g and its composition dependence micro-hardness and strength have been attributed to the inter-cluster correlation, and the enhancement of intra-cluster correlation due to minor alloying would contribute to the enhanced thermal glass stability. The experimental results were verified by alloying the Fe-B-based glassy alloy with Si and alloying the Fe-B-Si-based glassy alloy with ETMs (Zr, Hf, Nb, or Ta) and rare-earth metals (Y, Ce, Pr, Nd, Sm, Gd, or Dy). The experimental results correspond well with theoretical analysis. This study provides a novel understanding of the local structure-property correlation and minor alloying beneficial effects on amorphous alloys.