REM sleep is characterized by rapid eye movements, from which it gets its acronym, and is often accompanied by vivid visual dreams. Rapid eye movements occurring during REM sleep are proposed to represent gaze shifts in the virtual environment of dreams, while other studies suggest that they simply reflect random brainstem activity. In order to address this issue, we recorded from head direction (HD) cells in the anterodorsal nucleus of the thalamus (ADN), a population of neurons whose activity reports heading of the animal. Previous work has shown that during REM sleep, the population activity of HD cells is similar to that during actual navigation, in that it maintains a coherent representation of heading, i.e. a “virtual heading”. Because fast saccade-like eye movements are coupled to head movements during gaze shifts in awake freely-moving animals, we hypothesized that during REM sleep rapid eye movements may predict changes in virtual heading. To this end, we monitored eye movements during REM sleep while recording ensembles of HD cells from the ADN. We discovered that, during REM sleep, the direction of eye movements predicted the direction of the changes in virtual heading. Furthermore, the amplitude of rapid eye movements correlated with amplitude of changes in virtual heading. Importantly, such correlation between rapid eye movements and virtual heading was analogous to the relationship between fast saccade-like eye movements and the representation of heading in the ADN of awake mice. In conclusion, this study provides direct physiological evidence that rapid eye movements are coordinated with virtual heading during REM sleep, supporting the hypothesis that rapid eye movements represent gaze shifts in the virtual world of dreams during REM sleep. Furthermore, this study will facilitate future studies to elucidate the organization of the generative model during REM sleep, using rapid eye movements as its readout.