Grammatical Error Correction (GEC) faces a critical challenge concerning explainability, notably when GEC systems are designed for language learners. Existing research predominantly focuses on explaining grammatical errors extracted in advance, thus neglecting the relationship between explanations and corrections. To address this gap, we introduce EXGEC, a unified explainable GEC framework that integrates explanation and correction tasks in a generative manner, advocating that these tasks mutually reinforce each other. Experiments have been conducted on EXPECT, a recent human-labeled dataset for explainable GEC, comprising around 20k samples. Moreover, we detect significant noise within EXPECT, potentially compromising model training and evaluation. Therefore, we introduce an alternative dataset named EXPECT-denoised, ensuring a more objective framework for training and evaluation. Results on various NLP models (BART, T5, and Llama3) show that EXGEC models surpass single-task baselines in both tasks, demonstrating the effectiveness of our approach.