AlCoCrFeNi2.1 eutectic high-entropy alloy stands out for its remarkable mechanical properties, offering an excellent balance between strength and plasticity. For the first time, gas tungsten arc welding (GTAW) was applied to this as-cast alloy to investigate its weldability and associated microstructural evolution. A comprehensive analysis of the welded joint’s microstructure was performed using electron microscopy, electron backscatter diffraction (EBSD), synchrotron-based X-ray diffraction (SXRD), and thermodynamic simulations. The alloy's mechanical properties were characterized through microhardness mapping and tensile testing, which was integrated with digital image correlation (DIC) to provide insights into local deformation behavior. The welded joint, comprising the base material (BM), heat-affected zone (HAZ), and fusion zone (FZ), retained a eutectic structure with FCC and B2-type BCC phases. Variations in phase proportions arose due to thermal cycling during welding. BCC nanoprecipitates present in the BM were partially dissolved near the FZ boundary within the HAZ. Grain refinement in the FZ, driven by rapid solidification, contributed to increased hardness in this region. Despite these microstructural changes, tensile testing showed that the joints exhibited a favorable balance between strength and ductility, with failure consistently occurring in the BM. This work highlights the feasibility of using arc-based welding methods for high-entropy alloys, underscoring their potential for advanced structural applications.