Tidal currents and large-scale oceanic currents are known to modify ocean wave properties, causing extreme sea states that are a hazard to navigation. Recent advances in the understanding and modeling capability of open ocean currents have revealed the ubiquitous presence of eddies, fronts and filaments at scales 10 to 100∼km. Based on realistic numerical models, we show that these structures can be the main source of variability in significant wave heights at scales less than 200 km, including important variations down to 10 km. Model results are consistent with wave height variations along satellite altimeter tracks, resolved at scales larger than 50 km. The spectrum of significant wave heights is found to be of the order of 70〈Hs〉2/(g2〈Tm0,-1〉2) times the current spectrum, where〈Hs〉 is the spatially-averaged significant wave height, 〈Tm0,-1〉 is the energy-averaged period, and g is the gravity acceleration. This variability induced by currents has been largely overlooked in spite of its relevance for extreme wave heights and remote sensing.