The eutectic medium-entropy alloys CoFeNiTax (x = 0.4, 0.5, 0.6) were designed successfully based on binary eutectic systems and thermodynamics calculations in this study. With the increase of Ta content, the solidified microstructures evolved from hypoeutectic to full eutectic and finally to hypereutectic. The primary phases in the hypoeutectic and hypereutectic were FCC solid solution and C14-Laves phase, respectively. The solidified microstructures were coarsened and spheroidized by the heat treatment, and a high-density of needle-like Laves phase precipitated in the FCC phase of the CoFeNiTa0.4. The crystallographic orientation relationship between the precipitated phase and matrix phase was [2‾ 42‾ 3]Laves//[011]FCC, and the crystal plane (1 1‾ 1)FCC was almost parallel to (0 1‾ 12)Laves, just with a mismatch angle of about 6°. The compressive strength and fracture strain of the heat-treated alloys were within 2232∼2465 MPa and 22.5–32.8 %, respectively, being superior to most high-entropy alloys. The excellent combination of strength and toughness was attributed to the synergistic effects of various strengthening-toughening mechanisms, including the second-phase strengthening, the solid solution strengthening, the interface strengthening and toughening, and the twinning toughening.