Solar radiation prediction is an important process in ensuring optimal exploitation of solar energy power. Numerous models have been applied to this problem, such as numerical weather prediction models and artificial intelligence models. However, well-designed hybridization approaches that combine numerical models with artificial intelligence models to yield a more powerful model can provide a significant improvement in prediction accuracy. In this paper, we propose novel hybrid machine learning approaches that exploit auxiliary numerical data. The proposed hybrid methods invoke different machine learning paradigms, including feature selection, classification, and regression. Additionally, numerical weather prediction (NWP) models are used in the proposed hybrid models. Feature selection is used for feature space dimension reduction to reduce the large number of recorded parameters that affect estimation and prediction processes. The rough set theory is applied for attribute reduction and the dependency degree is used as a fitness function. We investigate the effect of the attribute reduction process with thirty different classification and prediction models in addition to the proposed hybrid model. Then, different machine learning models are constructed based on classification and regression techniques to predict solar radiation. Moreover, other hybrid prediction models are formulated to use the output of the numerical model of Weather Research and Forecasting (WRF) as learning elements in order to improve the prediction accuracy. The proposed methodologies are evaluated using a data set that is collected from different regions in Saudi Arabia.