High Entropy Alloys (HEAs) are new classes of structural metallic materials that show remarkable property combinations. Yet, often times interesting compositions are still found by trial and error. Here we show an “Effective Atomic Radii for Strength” (EARS) methodology, together with different semi-empirical and first-principle models, can be used to predict the extent of solid solution strengthening to discover and design new HEAs with unprecedented properties. We have designed a Cr₄₅Ni_27.5Co_27.5 alloy with a yield strength over 50% greater with equivalent ductility than the strongest HEA (Cr_33.3Ni_33.3Co_33.3) from the CrMnFeNiCo family reported to date. We show that values determined by the EARS methodology are more physically representative of multicomponent concentrated solid solutions. Our methodology permits high throughput, property-driven discovery and design of HEAs, enabling the development of future high-performance advanced materials for extreme environments.