<p>FeCoNi-based high-entropy amorphous alloys (HEAAs) have attracted considerable attention due to their outstanding soft magnetic properties and thermodynamic stability. This study investigates the effects of minor Cu addition on the non-isothermal crystallization kinetics and magnetic properties of (Fe₂CoNi)_80-<i>x</i>Si₁₀B₁₀Cu_<i>x</i> (<i>x</i> = 0 and 1) HEAAs. During non-isothermal annealing, the <i>ΔT</i> (<i>T</i>_<i>x2</i><i>—T</i>_<i>x1</i>) values of both HEAAs remained nearly constant, indicating that the high-entropy effect suppresses kinetic behavior variations induced by heating rate fluctuations. Furthermore, Cu addition effectively reduces the crystallization activation energy for the precipitation of the BCC phase, facilitating easier crystallization initiation. The Avrami exponent (<i>n</i>) significantly increases upon Cu addition, reaching a value exceeding 2.5 for Cu1, which demonstrates a transition to three-dimensional diffusion-controlled growth accompanied by accelerated nucleation rates. It is clearly stated that the addition of a small amount of Cu effectively regulates the crystallization behavior of the amorphous alloy, significantly reduces the crystallization activation energy of the BCC phase, and enhances the saturation magnetization and bending ductility of the alloy. These findings provide new ideas and methods for the development of high-performance amorphous alloy materials.</p>