While contemporary speech separation technologies adeptly process lengthy mixed audio waveforms, they are frequently challenged by the intricacies of real-world environments, including noisy and reverberant settings, which can result in artifacts or distortions in the separated speech. To overcome these limitations, we introduce SepALM, a pioneering approach that employs audio language models (ALMs) to rectify and re-synthesize speech within the text domain following preliminary separation. SepALM comprises four core components: a separator, a corrector, a synthesizer, and an aligner. By integrating an ALM-based end-to-end error correction mechanism, we mitigate the risk of error accumulation and circumvent the optimization hurdles typically encountered in conventional methods that amalgamate automatic speech recognition (ASR) with large language models (LLMs). Additionally, we have developed Chain-of-Thought (CoT) prompting and knowledge distillation techniques to facilitate the reasoning and training processes of the ALM. Our experiments substantiate that SepALM not only elevates the precision of speech separation but also markedly bolsters adaptability in novel acoustic environments.