Excellent castability, significantly refined microstructure, and good mechanical properties make eutectic high‐entropy alloys (EHEAs) a natural fit for rapid solidification processes, e.g., additive manufacturing. Previous investigations have focused on developing EHEAs through trial and error and mixing known binary eutectic materials. However, eutectic compositions obtained from near‐equilibrium conditions do not guarantee a fully eutectic microstructure under rapid solidifications. In this work, a thermodynamically guided high‐throughput framework is proposed to design EHEAs for rapid solidification. Empirical formulas derived from past experimental observations and thermodynamic computations are applied and considered phase growth kinetics under rapid solidification (skewed phase diagram). The designed alloy candidate, Co25.6Fe17.9Ni22.4Cr19.1Ta8.9Al6.1 (wt.%), contains nanostructured eutectic lamellar and shows a high Vickers hardness of 675 Hv. In addition to this specific composition, the alloy design toolbox enables the development of new EHEAs for rapid solidification without the limitation of previous knowledge.