In this paper, we introduce DiarizationLM, a framework to leverage large language models (LLM) to post-process the outputs from a speaker diarization system. Various goals can be achieved with the proposed framework, such as improving the readability of the diarized transcript, or reducing the word diarization error rate (WDER). In this framework, the outputs of the automatic speech recognition (ASR) and speaker diarization systems are represented as a compact textual format, which is included in the prompt to an optionally finetuned LLM. The outputs of the LLM can be used as the refined diarization results with the desired enhancement. As a post-processing step, this framework can be easily applied to any off-the-shelf ASR and speaker diarization systems without retraining existing components. Our experiments show that a finetuned PaLM 2-S model can reduce the WDER by rel. 55.5% on the Fisher telephone conversation dataset, and rel. 44.9% on the Callhome English dataset.