Biological electron transport is classically thought to occur over nanometre distances, yet recent studies suggest that electrical currents can run along centimetre-long cable bacteria. The phenomenon remains elusive, however, as currents have not been directly measured, nor have the conductive structures been identified. Here we demonstrate that cable bacteria conduct electrons over centimetre distances via highly conductive fibres embedded in the cell envelope. Direct electrode measurements reveal nanoampere currents in intact filaments up to 10.1 mm long (>2000 adjacent cells). A network of parallel periplasmic fibres displays a high conductivity (up to 79 S cm-1), explaining currents measured through intact filaments. Conductance rapidly declines upon exposure to air, but remains stable under vacuum, demonstrating that charge transfer is electronic rather than ionic. Our finding of a biological structure that efficiently guides electrical currents over long distances greatly expands the paradigm of biological charge transport and could enable new bio-electronic applications.