An exothermic welding apparatus and an exothermic welding method, belonging to the exothermic welding field are provided. The exothermic welding apparatus includes a mold, an igniter and an electronic starter, the mold has a holding space configured to accommodate an exothermic welding flux, the igniter includes a heating wire, a first conductor wire and a first connector, the heating wire is configured to ignite the exothermic welding flux directly, one end of the first conductor wire is electrically connected to the heating wire, the other end of the first conductor wire is electrically connected to the first connector, and the electronic starter cooperates with the first connector and is configured to supply power to the first connector. The exothermic welding apparatus can ignite an exothermic welding flux by supplying power with an electronic starter.