Code editing is a foundational task in software development, where its effectiveness depends on whether it introduces desired code property changes without changing the original code's intended functionality. Existing approaches often formulate code editing as an implicit end-to-end task, omitting the fact that code-editing procedures inherently consist of discrete and explicit steps, and thus suffer from suboptimal performance and lack of robustness and generalization. We introduce EditLord, a code editing framework that makes the code transformation steps explicit. Our key insight is to employ a language model (LM) as an inductive learner to extract code editing rules from the training code pairs as concise meta-rule sets. Such rule sets will be manifested for each training sample to augment them for finetuning or assist in prompting- and iterative-based code editing. EditLord outperforms the state-of-the-art by an average of 22.7% in editing performance and 58.1% in robustness while achieving 20.2% higher functional correctness, across critical software engineering and security applications, LM models, and editing modes.