Continuous long-term monitoring of electrocardiography (ECG) signals is crucial for the early detection of cardiac abnormalities such as arrhythmia. Non-clinical ECG recordings acquired by Holter and wearable ECG sensors often suffer from severe artifacts such as baseline wander, signal cuts, motion artifacts, variations on QRS amplitude, noise, and other interferences. Usually, a set of such artifacts occur on the same ECG signal with varying severity and duration, and this makes an accurate diagnosis by machines or medical doctors extremely difficult. Despite numerous studies that have attempted ECG denoising, they naturally fail to restore the actual ECG signal corrupted with such artifacts due to their simple and naive noise model. In this study, we propose a novel approach for blind ECG restoration using cycle-consistent generative adversarial networks (Cycle-GANs) where the quality of the signal can be improved to a clinical level ECG regardless of the type and severity of the artifacts corrupting the signal. To further boost the restoration performance, we propose 1D operational Cycle-GANs with the generative neuron model. The proposed approach has been evaluated extensively using one of the largest benchmark ECG datasets from the China Physiological Signal Challenge (CPSC-2020) with more than one million beats. Besides the quantitative and qualitative evaluations, a group of cardiologists performed medical evaluations to validate the quality and usability of the restored ECG, especially for an accurate arrhythmia diagnosis.