Ternary iron-boron-based bulk metallic glasses (BMGs) were explored exhibiting capability of thick amorphous casting at least 1 mm in rod diameter or 0.5 mm in plate thickness, excellent soft magnetic properties with saturation magnetization 1.56 T and coercivity smaller than 40 A/m, and electrical resistivity larger than 200 μΩ cm. The BMG alloys represented by the formulas MaFebBc are based on two simple selection rules: (1) M is an element with an atomic radius at least 130% that of Fe; (2) M possesses eutectic points with both Fe and B, and the M-Fe eutectic is at the Fe-rich end. Among more than 30 candidate M elements, Sc, Y, Dy, Ho, and Er fulfill BMG capability at the composition range, in at %, 3<a<10, 18<c<27, whereas a+b+c = 100. It is very remarkable that with a tiny addition of M, such as 4 at %, the critical cooling rate to form an amorphous state is abruptly lowered by more than four orders of magnitude as compared with Fe-B binary alloys, and a bulk amorphous state is achievable with only three elements (conventional ones 4–7 elements). These alloys are promising as core materials for transformers.