Every day we make decisions critical for adaptation and survival. We repeat actions with known consequences. But we also draw on loosely related events to infer and imagine the outcome of entirely novel choices. These inferential decisions are thought to engage a number of brain regions; however, the underlying neuronal computation remains unknown. Here, we use a multi-day cross-species approach in humans and mice to report the functional anatomy and neuronal computation underlying inferential decisions. We show that during successful inference, the mammalian brain uses a hippocampal prospective code to forecast temporally structured learned associations. Moreover, during resting behavior, coactivation of hippocampal cells in sharp-wave/ripples represent inferred relationships that include reward, thereby "joining-the-dots" between events that have not been observed together but lead to profitable outcomes. Computing mnemonic links in this manner may provide an important mechanism to build a cognitive map that stretches beyond direct experience, thus supporting flexible behavior.