To better understand how extreme climate events impact society, we need to increase the availability of accurate and comprehensive information about these impacts. We propose a method for building large-scale databases of climate extreme impacts from online textual sources, using LLMs for information extraction in combination with more traditional NLP techniques to improve accuracy and consistency. We evaluate the method against a small benchmark database created by human experts and find that extraction accuracy varies for different types of information. We compare three different LLMs and find that, while the commercial GPT-4 model gives the best performance overall, the open-source models Mistral and Mixtral are competitive for some types of information.