The present invention concerns a method and an apparatus for producing DRI (Direct Reduced Iron) utilizing a high-oxidation reducing gas containing carbon monoxide and hydrogen, derived directly or indirectly from the gasification of hydrocarbons or coal, with a high content of oxidants (H2O and CO2). The invention provides a more efficient method and plant comprising a reactor in which particulate material of iron ore comes into contact with a high temperature reducing gas to produce DRI, with lower investment and operating costs, avoiding the need for a fired heater for the reducing gas fed into the reduction reactor. The reducing gas is heated to a temperature above 700° C. in two steps, a first step at a temperature below about 400° C. to prevent the phenomenon of metal dusting, by exchange of sensible heat supplied by the stream of hot spent gas removed from the reduction reactor; and a second step by means of partial or total combustion with oxygen, maintaining the temperature of the combustion gas below the limits established by the construction materials of the combustion chamber.