Electroencephalography (EEG) allows the investigation of brain activity. However, neural signals often contain artefacts, hindering signal analysis. For example, eye-blink artefacts are particularly challenging due to their frequency overlap with neural signals. Artificial intelligence, particularly Variational Autoencoders (VAE), has shown promise in EEG artefact removal. This research explores the design and application of Convolutional VAEs for automatically detecting and removing eye blinks in EEG signals. The latent space of CVAE, trained on EEG topographic maps, is used to identify latent components that are selective for eye blinks. Receiver Operating Characteristic (ROC) curves and Area Under the Curve (AUC) are employed to evaluate the discriminative performance of each latent component. The most discriminative component, determined by the highest AUC, is modified to eliminate eye blinks. The evaluation of artefact removal involves visual inspection and Pearson correlation index assessment of the original EEG signal and the reconstructed clean version, focusing on the Fp1 and Fp2 channels most affected by eye-blink artefacts. Results indicate that the proposed method effectively removes eye blinks without significant loss of information related to the neural signal, demonstrating Pearson correlation values around 0.60 for each subject. The contribution to the knowledge offered by this research study is the design and application of a novel offline pipeline for automatically detecting and removing eye blinks from multi-variate EEG signals without human intervention.