Odour plumes in the wild are spatially complex and rapidly fluctuating structures carried by turbulent airflows1–4. To successfully navigate plumes in search of food and mates, insects must extract and integrate multiple features of the odour signal, including odour identity5, intensity6 and timing6–12. Effective navigation requires balancing these multiple streams of olfactory information and integrating them with other sensory inputs, including mechanosensory and visual cues9,12,13. Studies dating back a century have indicated that, of these many sensory inputs, the wind provides the main directional cue in turbulent plumes, leading to the longstanding model of insect odour navigation as odour-elicited upwind motion6,8–12,14,15. Here we show that Drosophila melanogaster shape their navigational decisions using an additional directional cue—the direction of motion of odours—which they detect using temporal correlations in the odour signal between their two antennae. Using a high-resolution virtual-reality paradigm to deliver spatiotemporally complex fictive odours to freely walking flies, we demonstrate that such odour-direction sensing involves algorithms analogous to those in visual-direction sensing16. Combining simulations, theory and experiments, we show that odour motion contains valuable directional information that is absent from the airflow alone, and that both Drosophila and virtual agents are aided by that information in navigating naturalistic plumes. The generality of our findings suggests that odour-direction sensing may exist throughout the animal kingdom and could improve olfactory robot navigation in uncertain environments. Odour motion contains valuable directional information that is absent from the airflow alone, and Drosophila use this directional information to shape their navigational decisions.