A fundamental unresolved problem in neuroscience is how the brain associates in memory events that are separated in time. Here, we propose that reactivation-induced synaptic plasticity can solve this problem. Previously, we reported that the reinforcement signal dopamine converts hippocampal spike timing-dependent depression into potentiation during continued synaptic activity (Brzosko et al., 2015). Here, we report that postsynaptic bursts in the presence of dopamine produce input-specific LTP in mouse hippocampal synapses 10 min after they were primed with coincident pre- and post-synaptic activity (post-before-pre pairing; Δt = -20 ms). This priming activity induces synaptic depression and sets an NMDA receptor-dependent silent eligibility trace which, through the cAMP-PKA cascade, is rapidly converted into protein synthesis-dependent synaptic potentiation, mediated by a signaling pathway distinct from that of conventional LTP. This synaptic learning rule was incorporated into a computational model, and we found that it adds specificity to reinforcement learning by controlling memory allocation and enabling both 'instructive' and 'supervised' reinforcement learning. We predicted that this mechanism would make reactivated neurons activate more strongly and carry more spatial information than non-reactivated cells, which was confirmed in freely moving mice performing a reward-based navigation task.