New eutectic high-entropy alloys based on novel (CoqCrvFewMoyNiz)(100-x)Al-x alloy systems were designed using both thermodynamic and computational approaches. After considering 324 equilibrium diagrams, ten potential eutectic compositions were determined to possess a eutectic point comprising FCC and B2 phases. (Co40Cr10Fe5Mo5Ni40)(82,2)Al-17.8 was found to have a fully eutectic structure through experimental analysis, which had a negligible error (0.23%) compared to that of the computational modeling. The XRD patterns showed that the alloy was composed of only FCC and B2 phases (with volume fractions of 73.4% and 26.6%, respectively) and did not contain sigma phase, which was predicted by the computational model to appear at low temperatures. Among all other alloys, the hypereutectic (18 at% Al) alloy exhibited the highest compressive yield strength (729 MPa) and ultimate compressive strength (2844 MPa), and the hypoeutectic (16 at% Al) alloy had the highest compressive ductility (similar to 39%). For all fabricated alloys (hypoeutectic, eutectic, and hypereutectic), the compressive strength and strain exceeded 2514 MPa and 27%, respectively.