Ocean wind waves follow shifts in atmospheric circulation and wind regimes caused by climate change and variability. We use a wave model (WAM) forced by winds from an Earth system model (EC-Earth) to study the evolution of global wave climate in terms of trends in wind speed and wave height, their rates and anomalies over the 250 years. Historical period and future scenarios (RCP8.5 and RCP4.5) are calculated within the fifth phase of the Coupled Model Intercomparison Project. Both scenarios indicate a future increase of wind speed and wave height in the Arctic and Southern Ocean and a decrease in the Pacific Ocean. Some regions, e.g., the North Atlantic show a change of sign from currently positive to negative trends in this century. Swell dominated regions, connected to the Southern Ocean show opposite trends for winds and waves. Calculated trends are evaluated taking into account natural variability estimated from a simulation with pre–industrial climate. We conclude that projected wave heights are still within natural variability, whereas wind speed exceeds it in the Arctic and Southern Ocean. Probability estimates show that extreme winds and waves become more dominant in the Southern Hemisphere, Arctic and Indian Ocean. Low and medium winds and waves are highly probable in the North and Equatorial Atlantic and Pacific.