A method of welding at least two workpieces (12,14) together by metallurgically joining faying surfaces of the workpieces (12,14), the method characterized by: placing the workpieces (12,14) together so that the faying surfaces thereof face each other and a joint region is defined, the joint region comprising an intersurface portion defined by and between the faying surfaces and immediately adjacent surfaces of the workpieces (12,14) that remain exposed after the workpieces (12,14) are placed together; and characterized by the following steps: conducting forward and aft hybrid welding processes in sequence along the joint region, the forward hybrid welding process comprising projecting a forward laser beam onto the joint region to cause a projection of the forward laser beam to travel along the joint region and penetrate the intersurface portion of the joint region and further comprising directing a forward electric arc onto the projection of the forward laser beam while feeding a first weld filler metal wire having a first diameter into the forward electric arc to form a forward weld pool that solidifies to form a weldment in the joint region, the aft hybrid welding process comprising projecting an aft laser beam onto the weldment to cause a projection of the aft laser beam to travel along and penetrate the weldment and further comprising directing an aft electric arc onto the projection of the aft laser beam while feeding a second weld filler metal wire having a second diameter into the aft electric arc to form an aft weld pool, the second diameter of the second weld filler metal wire being greater than the first diameter of the first weld filler metal wire, the forward and aft laser beam projections (38,42) being spaced apart along the joint region and the forward and aft electric arcs (36,56) being spaced apart along the joint region so as to cause the aft weld pool formed by the aft hybrid welding process to cascade onto, remelt and intermix with the weldment to form a combined weld pool; and then cooling the combined weld pool to form a weld joint within the joint region that metallurgically joins the workpieces (12,14) to yield a welded assembly. placing the workpieces (12,14) together so that the faying surfaces thereof face each other and a joint region is defined, the joint region comprising an intersurface portion defined by and between the faying surfaces and immediately adjacent surfaces of the workpieces (12,14) that remain exposed after the workpieces (12,14) are placed together; and characterized by the following steps: conducting forward and aft hybrid welding processes in sequence along the joint region, the forward hybrid welding process comprising projecting a forward laser beam onto the joint region to cause a projection of the forward laser beam to travel along the joint region and penetrate the intersurface portion of the joint region and further comprising directing a forward electric arc onto the projection of the forward laser beam while feeding a first weld filler metal wire having a first diameter into the forward electric arc to form a forward weld pool that solidifies to form a weldment in the joint region, the aft hybrid welding process comprising projecting an aft laser beam onto the weldment to cause a projection of the aft laser beam to travel along and penetrate the weldment and further comprising directing an aft electric arc onto the projection of the aft laser beam while feeding a second weld filler metal wire having a second diameter into the aft electric arc to form an aft weld pool, the second diameter of the second weld filler metal wire being greater than the first diameter of the first weld filler metal wire, the forward and aft laser beam projections (38,42) being spaced apart along the joint region and the forward and aft electric arcs (36,56) being spaced apart along the joint region so as to cause the aft weld pool formed by the aft hybrid welding process to cascade onto, remelt and intermix with the weldment to form a combined weld pool; and then cooling the combined weld pool to form a weld joint within the joint region that metallurgically joins the workpieces (12,14) to yield a welded assembly.