Ions dissolved in aqueous media play a fundamental role in plants, animals, and humans. Therefore, the in situ quantification of the ion concentration in aqueous media is gathering relevant interest in several fields including biomedical diagnostics, environmental monitoring, healthcare products, water and food test and control, agriculture industry and security. The fundamental limitation of the state-of-art transistor-based approaches is the intrinsic trade-off between sensitivity, ion concentration range and operating voltage. Here we show a current-driven configuration based on organic electrochemical transistors that overcomes this fundamental limit. The measured ion sensitivity exceeds by one order of magnitude the Nernst limit at an operating voltage of few hundred millivolts. The ion sensitivity normalized to the supply voltage is larger than 1200 mV V-1 dec-1, which is the largest value ever reported for ion-sensitive transistors. The proposed approach is general and can be extended to any transistor technology, thus opening opportunities for high-performance bioelectronics.