The object of the patent is a sustainable method and a system for cleaning impurities, mainly hydrogen sulphide, and upgrading of biogas having hydrogen sulphide concentration up to 2% (20,000 ppmv), preferably produced in wastewater treatment plants (WWTPs) to biomethane, wherein the system comprises a counter-current, non-pressurized physical absorption bubble column having a high influent liquid-to-gas flow ratio L I /G higher than 1 and preferably equal or higher than 3 and equal or lower than 10, for achieving a simultaneous removal of hydrogen sulphide and carbon dioxide. The present system may be inserted for instance on an existing wastewater treatment plant, in such a way that the wash water is the primary treated wastewater of the plant, and preferably the biogas to be upgraded is produced in the anaerobic digesters of the plant itself, and also includes means for regenerating the used wash water by the biological reactor of the plant itself used for the secondary treatment.