End-to-end speech-to-speech translation (S2ST) systems typically struggle with a critical data bottleneck: the scarcity of parallel speech-to-speech corpora. To overcome this, we introduce RosettaSpeech, a novel zero-shot framework trained exclusively on monolingual speech-text data augmented by machine translation supervision. Unlike prior works that rely on complex cascaded pseudo-labeling, our approach strategically utilizes text as a semantic bridge during training to synthesize translation targets, thereby eliminating the need for parallel speech pairs while maintaining a direct, end-to-end inference pipeline. Empirical evaluations on the CVSS-C benchmark demonstrate that RosettaSpeech achieves state-of-the-art zero-shot performance, surpassing leading baselines by significant margins - achieving ASR-BLEU scores of 25.17 for German-to-English (+27% relative gain) and 29.86 for Spanish-to-English (+14%). Crucially, our model effectively preserves the source speaker's voice without ever seeing paired speech data. We further analyze the impact of data scaling and demonstrate the model's capability in many-to-one translation, offering a scalable solution for extending high-quality S2ST to "text-rich, speech-poor" languages.