Bacterial persistence is a state in which a sub-population of dormant cells, or `persisters', tolerates antibiotic treatment. Bacterial persisters have been implicated in biofilms and in chronic and recurrent infections. Despite this clinical relevance, there are currently no viable means for eradicating persisters. Here we show that specific metabolic stimuli enable the killing of both Gram-negative (Escherichia coli) and Gram-positive (Staphylococcus aureus) persisters with aminoglycosides. This potentiation is aminoglycoside-specific, it does not rely on growth resumption and it is effective in both aerobic and anaerobic conditions. It proceeds by the generation of a proton-motive force which facilitates aminoglycoside uptake. Our results demonstrate that persisters, although dormant, are primed for metabolite uptake, central metabolism and respiration. We show that aminoglycosides can be used in combination with specific metabolites to treat E. coli and S. aureus biofilms. Furthermore, we demonstrate that this approach can improve the treatment of chronic infections in a mouse urinary tract infection model. This work establishes a strategy for eradicating bacterial persisters that is based on metabolism, and highlights the importance of the metabolic environment to antibiotic treatment.