A welding method and apparatus for welding workpieces together by conducting a forward hybrid welding process on a joint region that includes a weld seam defined by and between faying surfaces of the workpieces, and then conducting an aft hybrid welding process on the joint region. The forward hybrid welding process simultaneously causes a forward laser beam and a forward electric arc to travel along the joint region, which in combination penetrates the weld seam and forms a weld pool that solidifies to form a weldment. The aft hybrid welding process utilizes an aft electric arc and an aft laser beam to produce a second weld pool that remelts and mixes with the weldment. On cooling, a weld joint is formed that is capable of deeply penetrating the weld seam of the joint region.