A method of welding reinforcement steel bars (rebar) and assembly of fusion-welded rebar into panel assemblies that are self-stabilizing to withstand the rigors of transport to and positioning within construction sites. The rebar welding method generates fusion welds in such a manner that the weld imparts stability and strength to the welded rebar assemblies. The rebar welds permit the assembling of larger and more varied rebar panel configurations without the need for tie wire or other coupling devices. Further, the welded panels allow positioning of large rebar configurations, insuring that the spacing of the individual bars exceeds all required tolerances. The self-stabilizing fusion rebar welding process allows a more efficient, flexible and rapid method of rebar panel construction by using assembly systems on mobilized trailers or at stationary locations.