Various artifacts and noises with physiological and non-physiological causes often appear in electroencephalogram (EEG) signals. Because of its magnitude, eyeblink is considered to have the largest impact on EEG analysis among these artifacts. The interference of the eyeblink artifacts leads to a faulty interpretation of brain activity. A novel approach is presented to estimate eyeblink artifacts using a Continuous Wavelet Transform (CWT) filter bank. The CWT filter bank is used to decompose the independent components (ICs) obtained from input EEG signals, and the resulting wavelet independent components (wICs) are then thresholded using a universal threshold to produce the eyeblink artifacts. The estimated eyeblink artifact is then applied to the quadratic regression method to clean the contaminated EEG signals. A publicly available semi-simulated dataset is used to test the proposed method. To determine how well algorithms eliminate eyeblink artifacts and how much the EEG signals are altered after artifact rejection, four performance measurements (Root Mean Squared Error, Power Spectrum Distortion, Signal-to-Artifact Ratio, and Correlation Coefficient) are used. The ICA-CWT could be a suitable method for real-time EEG-based systems because it is fully automated, requires no human interaction, and is computationally fast.