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Electrochemical batteries are ubiquitous devices in our society. When they are employed in mission-critical applications, the ability to precisely predict the end of discharge under highly variable environmental and operating conditions is of paramount importance in order to support operational decision-making. While there are accurate predictive models of the processes underlying the charge and discharge phases of batteries, the modelling of ageing and its effect on performance remains poorly understood. Such a lack of understanding often leads to inaccurate models or the need for time-consuming calibration procedures whenever the battery ages or its conditions change significantly. This represents a major obstacle to the real-world deployment of efficient and robust battery management systems. In this paper, we propose for the first time an approach that can predict the voltage discharge curve for batteries of any degradation level without the need for calibration. In particular, we introduce Dynaformer, a novel Transformer-based deep learning architecture which is able to simultaneously infer the ageing state from a limited number of voltage/current samples and predict the full voltage discharge curve for real batteries with high precision. Our experiments show that the trained model is effective for input current profiles of different complexities and is robust to a wide range of degradation levels. In addition to evaluating the performance of the proposed framework on simulated data, we demonstrate that a minimal amount of fine-tuning allows the model to bridge the simulation-to-real gap between simulations and real data collected from a set of batteries. The proposed methodology enables the utilization of battery-powered systems until the end of discharge in a controlled and predictable way, thereby significantly prolonging the operating cycles and reducing costs.