Electroencephalogram (EEG) signals suffer substantially from motion artifacts even in ambulatory settings. Signal processing techniques for removing motion artifacts from EEG signals have limitations, and the potential of classical or deep machine-learning algorithms for this task remains largely unexplored. We propose Attention-Guided Operational CycleGAN (AGO-CycleGAN), a novel CycleGAN-based framework to remove motion artifacts and enhance the quality of corrupted EEG signals. It incorporates self-generative operational neurons and an attention-guided Feature Pyramid Network with modified bottlenecks as generators and PatchGAN-based discriminators. AGO-CycleGAN was trained and tested on a single-channel EEG dataset from 23 subjects, using a subject-independent Jackknife cross-validation approach. It outperformed other methods and was evaluated through qualitative and quantitative analysis, employing robust metrics in both temporal and frequency domains. The results indicate its effectiveness in restoring EEG signals affected by severe motion artifacts. AGO-CycleGAN achieves state-of-the-art EEG restoration performance in the temporal domain, gaining improvements in signal-to-noise ratio (ΔSNR) and temporal correlation (ηtemp) by 26.497 dB and 87.2%, respectively. It also showed excellent performance in preserving the spectral EEG components (delta, theta, alpha, beta, and gamma), evaluated through band power ratio before and after restoration. Spectral correlation (ηspec) improved by 93.5% after cleaning the motion artifacts. Qualitative evaluations showed excellently reconstructed clean EEG waveforms upon restoration. Spectral restoration visualized through Power Spectral Density (PSD) plots and per-band topographic maps showed a uniform removal of high-power motion artifact components throughout the spectrum. AGO-CycleGAN significantly outperformed existing techniques in EEG artifact removal and can be extended to multi-channel EEG systems.