This paper combines random forests with physics-based models to forecast the electricity output of the Mutriku wave farm on the Bay of Biscay. The period analysed was 2014–2016, and the forecast horizon was 24 h in 4-h steps. The Random Forest (RF) machine-learning technique was used, with three sets of inputs: i) the electricity generated at Mutriku, ii) the wave energy flux (WEF) prediction made by the ECMWF wave model at Mutriku’s nearest gridpoint, and iii) ocean and atmospheric data for the Bay of Biscay. For this last input, extended empirical orthogonal functions (EOFs) were calculated to reduce the dimensionality of these data, while retaining most of the information. The forecasts are evaluated using the R-Squared, Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The model easily outperforms a persistence forecast at 8–10 h and beyond. The most accurate forecasts are achieved by using all three of these inputs. This approach may help to effectively integrate wave farms into the electricity market.