The present invention relates to a method and plant for the depuration of leachate from municipal solid waste landfills or of comparably similar waste liquors. The waste liquor is subjected to an anaerobic treatment with production of biogas and precipitation of heavy metals. An anoxic denitrification step is then carried out, followed by a biological oxidation-nitrification step in which the removal of the organic pollutant components present in the percolate is completed, and the almost complete oxidation of ammonia to nitrate ion for the subsequent reduction in anoxic conditions of the nitrate ion to nitrogen is assured. If so required by the limits imposed on the effluent, the effectiveness of removal of the organic substances contained in the percolate can be enhanced by the addition of suitably proportioned amounts of powdered activated carbon into the biological oxidation reactor or by means of a filtration of the effluent on granular activated carbon.