Electroencephalography (EEG) is a critical tool in neuroscience and clinical diagnostics, offering valuable insights into brain activity. However, EEG signals are often contaminated by ocular artifacts, which can significantly distort the data, leading to potential misinterpretations. This study introduces a novel method for removing ocular artifacts from EEG signals using a combination of Discrete Wavelet Transform (DWT) and Savitzky-Golay (SG) filter. The proposed method effectively separates the EEG signal into multiple subbands using DWT, followed by the application of the SG filter to the contaminated subbands to remove artifacts while preserving the integrity of the original EEG signal. The performance of the proposed method is evaluated using a publicly available EEG dataset. Two performance metrics (signal-to-noise ratio improvement, and percentage reduction of correlation coefficient) are used to test the DWT-SG method. The results show superior artifact removal capabilities and lower computational complexity compared to traditional methods. The results demonstrate that the DWT-SG approach has an average SNRI and η values of 10.367 dB and 25.26%.