Recommender systems (RSs) play a pervasive role in today's online services, yet their closed-loop nature constrains their access to open-world knowledge. Recently, large language models (LLMs) have shown promise in bridging this gap. However, previous attempts to directly implement LLMs as recommenders fall short in meeting the requirements of industrial RSs, particularly in terms of online inference latency and offline resource efficiency. Thus, we propose REKI to acquire two types of external knowledge about users and items from LLMs. Specifically, we introduce factorization prompting to elicit accurate knowledge reasoning on user preferences and items. We develop individual knowledge extraction and collective knowledge extraction tailored for different scales of scenarios, effectively reducing offline resource consumption. Subsequently, generated knowledge undergoes efficient transformation and condensation into augmented vectors through a hybridized expert-integrated network, ensuring compatibility. The obtained vectors can then be used to enhance any conventional recommendation model. We also ensure efficient inference by preprocessing and prestoring the knowledge from LLMs. Experiments demonstrate that REKI outperforms state-of-the-art baselines and is compatible with lots of recommendation algorithms and tasks. Now, REKI has been deployed to Huawei's news and music recommendation platforms and gained a 7% and 1.99% improvement during the online A/B test.