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The invention relates to a bioelectrochemical reactor which comprises: - an anode chamber having at least two bioanodes and an anodic electrolyte comprising anodic electroactive microorganisms, - a cathode chamber comprising at least one biocathode, and a cathodic electrolyte comprising cathodic electroactive microorganisms, - the anode chamber being separated from the cathode chamber by, running from the anode chamber to the cathode chamber, a cation exchange membrane and an anion exchange membrane, said cation and anion exchange membranes being separated from each other by an inter-membrane chamber (30), and - means for applying a potential difference between the interconnected bioanodes and the biocathode/biocathodes, the bioanodes and biocathode/biocathodes having active surfaces such that the total active surface of the biocathode/biocathodes is greater than the total active surface of the two bioanodes. The invention also relates to a method for regenerating the activity of the bioanodes of the reactor and to the use of said reactor for the electrosynthesis of organic acids and/or alcohols from organic waste.