Despite the remarkable success of Large Language Models (LLMs) in Machine Translation (MT), the scarcity of high-quality parallel corpora and the prohibitive cost of their acquisition constrain scalability. To this end, we propose Learning to Translate by Translating (LTT), an LLM-driven dual-learning framework that enables autonomous translation, achieving an 80.42% performance improvement over the base model. By adapting the cycle-consistency principle to the generative paradigm, LTT eliminates the need for parallel data. It employs a robust semantic-aware reward function that balances adequacy with reconstruction fidelity, effectively mitigating the reward hacking issues inherent in traditional unsupervised MT. Relying solely on monolingual data, our 8B model consistently outperforms significantly larger models (70B+) in low-resource settings and achieves parity with state-of-the-art supervised baselines on mainstream benchmarks. LTT thus offers a scalable, data-efficient paradigm for autonomous machine translation.