Cross-document relation extraction (RE) infers entity relationships by integrating multi-document information, which better aligns with real-world scenarios. Existing research primarily focuses on evidence extraction to support relation reasoning, yet due to fragmented information across documents, extracted evidence often fails to cover complete reasoning chains. Although recent studies have attempted to supplement evidence with external information, these approaches neglect two critical issues: the relevance between external information and reasoning chains, and rigorous validation of external information validity. This neglect inevitably introduces irrelevant data or noise into the reasoning process. To address these limitations, we propose KA-CDRE, a novel Knowledge-Augmented method for Cross-Document RE. It includes two components: 1) a Reasoning-Chain-Aware Knowledge Constructor, which leverages bridge entities to acquire external knowledge that potentially populates critical nodes within reasoning chains; 2) a Semantics-Aware Knowledge Selector, which employs entity-pair contextual semantics to filter acquired external knowledge, suppressing noise while enabling effective knowledge injection. Extensive experiments on the CodRED dataset demonstrate the effectiveness of our method. In the open setting, KA-CDRE outperforms state-of-the-art methods by 3.49% in F1 and 3.95% in AUC. In the closed setting, it attains comparable performance gains, significantly outperforming all benchmarks.