We introduce a simple method for text style transfer that frames style transfer as denoising: we synthesize a noisy corpus and treat the source style as a noisy version of the target style. To control for aspects such as preserving meaning while modifying style, we propose a reranking approach in the data synthesis phase. We evaluate our method on three novel style transfer tasks: transferring between British and American varieties, text genres (formal vs. casual), and lyrics from different musical genres. By measuring style transfer quality, meaning preservation, and the fluency of generated outputs, we demonstrate that our method is able both to produce high-quality output while maintaining the flexibility to suggest syntactically rich stylistic edits.