Nowadays the usage of portable electroencephalography (EEG) recorded systems are raised for recording of neuro activities of the brain, which are useful in clinical diagnosis such as brain–computer interface (BCI) applications. The eye movements or blinks are unavoidable activities, which reflects the electrooculogram (EOG) artifacts in the recorded EEG signals, which leads deceptive interpretation of the underlying brain state. In this paper a novel framework is proposed as Variational Mode Extraction (VME) method is integrated with Generalized Moreau Envelope Total Variation (GMETV) technique to filter the EOG artifacts. Initially, the contaminated EEG is applied to the VME method which extracts the EOG artifact segment. Then, this EOG artifact segment is given to the GMETV technique and it separates the wanted component of the EEG residue from the EOG artifact segment. The EEG residue is added back to the non EOG artifact segment signal which gives the final denoised EEG. Matlab simulations are done on both simulated and real time EEG databases to evolute the proposed VME-GMETV technique performance in terms of Relative Root Mean Square Error (RRMSE), Correlation Coefficient (CC) and Mean Absolute Error (MAE). From the experimental results, the proposed technique is outperformed the existing methods by averaged low RRMSE (0.1557), MAE (5.0714e−04) and averaged high CC (0.9695).