The task of Grammatical Error Correction (GEC) has been extensively studied for the English language. However, its application to low-resource languages, such as Ukrainian, remains an open challenge. In this paper, we develop sequence tagging and neural machine translation models for the Ukrainian language as well as a set of algorithmic correction rules to augment those systems. We also develop synthetic data generation techniques for the Ukrainian language to create high-quality human-like errors. Finally, we determine the best combination of synthetically generated data to augment the existing UA-GEC corpus and achieve the state-of-the-art results of 0.663 F0.5 score on the newly established UA-GEC benchmark. The code and trained models will be made publicly available on GitHub and HuggingFace.