Large language models (LLMs) have made significant advancements in code-related tasks, yet many LLMs treat code as simple sequences, neglecting its structured nature. We introduce AST-T5, a novel pretraining paradigm that leverages the Abstract Syntax Tree (AST) for enhanced code generation, transpilation, and understanding. Using dynamic programming, our AST-Aware Segmentation retains code structure, while our AST-Aware Span Corruption objective equips the model to reconstruct various code structures. Unlike other models, AST-T5 avoids complex program analyses or architectural changes, so it integrates seamlessly with any encoder-decoder Transformer. Evaluations show that AST-T5 consistently outperforms similar-sized LMs across various code-related tasks including HumanEval and MBPP. Structure-awareness makes AST-T5 particularly powerful in code-to-code tasks, surpassing CodeT5 by 2 points in exact match score for the Bugs2Fix task and by 3 points in exact match score for Java-C# Transpilation in CodeXGLUE. Our code and model are publicly available at https://annonymized.