Drought is a stochastic natural feature that arises due to intense and persistent shortage of precipitation. Its impact is mostly manifested as agricultural and hydrological droughts following an initial meteorological phenomenon. Drought prediction is essential because it can aid in the preparedness and impact-related management of its effects. This study considers the drought forecasting problem by developing a hybrid predictive model using a denoised empirical mode decomposition (EMD) and a deep belief network (DBN). The proposed method first decomposes the data into several intrinsic mode functions (IMFs) using EMD, and a reconstruction of the original data is obtained by considering only relevant IMFs. Detrended fluctuation analysis (DFA) was applied to each IMF to determine the threshold for robust denoising performance. Based on their scaling exponents, irrelevant intrinsic mode functions are identified and suppressed. The proposed method was applied to predict different time scale drought indices across the Colorado River basin using a standardized streamflow index (SSI) as the drought index. The results obtained using the proposed method was compared with standard methods such as multilayer perceptron (MLP) and support vector regression (SVR). The proposed hybrid model showed improvement in prediction accuracy, especially for multi-step ahead predictions.