The machine for closing the tail end of logs of web material, includes an advancing path of the logs and, along the log advancing path, a tail end unwinding, positioning and sealing station. The tail end unwinding, positioning and sealing station includes an aperture that extends downwards from an inlet under the log advancing path. At least a first Coanda effect nozzle is placed at the inlet of the aperture, to generate a flow of air adapted to draw into the aperture the tail end of a log that is in the tail end unwinding, positioning and sealing station.