This paper proposes an automatic eyeblink artifacts removal method from corrupted-EEG signals using discrete wavelet transform (DWT) and meta-heuristically optimized threshold. The novel idea of thresholding approximation-coefficients (ACs) instead of detail-coefficients (DCs) of DWT of EEG in a backward manner is proposed for the first time for the removal of eyeblink artifacts. EEG is very sensitive and easily gets affected by eyeblink artifacts. First, the eyeblink corrupted EEG signals are identified using support vector machine (SVM) as a classifier. Then the corrupted EEG signal is decomposed using DWT up to the sixth level. Both the mother wavelet and the level of decomposition are selected using appropriate techniques. Then the ACs are thresholded in backward manner using the optimum threshold values followed by inverse DWT operation to reconstruct the original EEG signal. The AC at level 6 is thresholded and is used in IDWT with DC to get back the AC at level 5. Likewise, the backward thresholding of the ACs followed by IDWT is continued till the artifact free EEG signal is reconstructed at level 1. The optimum values of the thresholds of the ACs at different levels are optimized using two meta-heuristic algorithms, particle swarm optimization (PSO) and grey wolf optimization (GWO) for comparison. The results reveal that the proposed methodology is superior to the recently reported methods in terms of average correlation coefficient (CC) which states that the proposed method is better in terms of the quality of reconstruction in addition to being fully automatic.