There is evidence that transcranial direct current stimulation (tDCS) can improve learning performance. Arguably, this effect is related to long term potentiation (LTP), but the precise biophysical mechanisms remain unknown. We propose that direct current stimulation (DCS) causes small changes in postsynaptic membrane potential during ongoing endogenous synaptic activity. The altered voltage dynamics in the postsynaptic neuron then modify synaptic strength via the machinery of endogenous voltage-dependent Hebbian plasticity. This hypothesis predicts that DCS should exhibit Hebbian properties, namely pathway specificity and associativity. We studied the effects of DCS applied during the induction of LTP in the CA1 region of rat hippocampal slices and using a biophysical computational model. DCS enhanced LTP, but only at synapses that were undergoing plasticity, confirming that DCS respects Hebbian pathway specificity. When different synaptic pathways cooperated to produce LTP, DCS enhanced this cooperation, boosting Hebbian associativity. Further slice experiments and computer simulations support a model where polarization of postsynaptic pyramidal neurons drives these plasticity effects through endogenous Hebbian mechanisms. The model is able to reconcile several experimental results by capturing the complex interaction between the induced electric field, neuron morphology, and endogenous neural activity. These results suggest that tDCS can enhance associative learning. We propose that clinical tDCS should be applied during tasks that induce Hebbian plasticity to harness this phenomenon, and that the effects should be task specific through their interaction with endogenous plasticity mechanisms. Models that incorporate brain state and plasticity mechanisms may help to improve prediction of tDCS outcomes. •DCS boost LTP and Hebbian associativity, while maintaining pathway specificity.•Effects are consistent with somatic polarization of postsynaptic pyramidal cells.•A computational model captures the dependence on endogenous synaptic activity.•tDCS should be applied during training that induces Hebbian plasticity.•Effects should be specific to trained tasks.