This paper proposes CrossLink, a novel framework for cross-domain link prediction. CrossLink learns the evolution pattern of a specific downstream graph and subsequently makes pattern-specific link predictions. It employs a technique called conditioned link generation, which integrates both evolution and structure modeling to perform evolution-specific link prediction. This conditioned link generation is carried out by a transformer-decoder architecture, enabling efficient parallel training and inference. CrossLink is trained on extensive dynamic graphs across diverse domains, encompassing 6 million dynamic edges. Extensive experiments on eight untrained graphs demonstrate that CrossLink achieves state-of-the-art performance in cross-domain link prediction. Compared to advanced baselines under the same settings, CrossLink shows an average improvement of 11.40% in Average Precision across eight graphs. Impressively, it surpasses the fully supervised performance of 8 advanced baselines on 6 untrained graphs. Project Page is https://zjunet.github.io/CrossLink/