In the frame of the circular economy, welding of Ni-based superalloys has gained increasing importance when applied, for instance, to repairing highly expensive components widely used in strategical sectors, such as the defense and aerospace industries. However, correct process parameters avoiding metallurgical defects and premature failures need to be known. To reach this goal, Inconel 625 butt-welded joints were produced by CO2 laser beam welding and different combinations of process parameters. The experimental investigation was carried out with three parameters in two levels with an L4 orthogonal array. Laser power, welding speed, and shielding gas flow rate were varied, and the results were reported in terms of mechanical properties, such as microhardness, tensile strength, distortion, residual stress, and weld bead geometry, and metallurgy. At a lower welding speed of 1 m/min, the full penetration was observed for 3.0 kW and 3.3 kW laser powers. However, sound welds (porosity-free) were produced with a laser power of 3.3 kW. Overall, the obtained full-penetration specimens showed a tensile strength comparable with that of the parent material with residual stresses and distortions increasing with the increase in heat input.