Electroencephalography is frequently used for diagnostic evaluation of various brain-related disorders due to its excellent resolution, non-invasive nature and low cost. However, manual analysis of EEG signals could be strenuous and a time-consuming process for experts. It requires long training time for physicians to develop expertise in it and additionally experts have low inter-rater agreement (IRA) among themselves. Therefore, many Computer Aided Diagnostic (CAD) based studies have considered the automation of interpreting EEG signals to alleviate the workload and support the final diagnosis. In this paper, we present an automatic binary classification framework for brain signals in multi-channel EEG recordings. We propose to use Wavelet Packet Decomposition (WPD) techniques to decompose the EEG signals into frequency sub-bands and extract a set of statistical features from each of the selected coefficients. Moreover, we propose a novel method to reduce the dimension of the feature space without compromising the quality of the extracted features. The extracted features are classified using different Gradient Boosting Decision Tree (GBDT) based classification frameworks, which are CatBoost, XGBoost and LightGBM. We used Temple University Hospital EEG Abnormal Corpus V2.0.0 to test our proposed technique. We found that CatBoost classifier achieves the binary classification accuracy of 87.68%, and outperforms state-of-the-art techniques on the same dataset by more than 1% in accuracy and more than 3% in sensitivity. The obtained results in this research provide important insights into the usefulness of WPD feature extraction and GBDT classifiers for EEG classification.