Being able to predict the output power of wind turbines and wind farms is crucial in the process of integrating such stochastic energy sources with power systems. To support stakeholders in short- and mid-term wind power prediction, a novel data-driven Machine Learning based approach is proposed. This approach relies on three Gradient Boosting (GB) regressor implementations. The novelty of our approach is also manifested in the fact, that it is respectively based on the use of MERRA-2 reanalysis data and GEOS FP meteorological forecasts in models training and wind power prediction. It makes the short- and mid-term prediction unique in enriching the results even for time horizon of 240 h with resolution of 1 h. The data preprocessing and cleaning, feature engineering, and training, testing and validation of the models are presented in details. The performances of the models and prediction accuracy are evaluated relying on a few absolute and relative error measures. The proposed methodology is implemented in the output power prediction of a wind turbine located in Poland. The results of predictions are compared with other Machine Learning algorithms. The results show that proposed GB implementations can capture accepted accuracy of prediction and outperform other investigated algorithms.