Large language model (LLM)-based multi-agent systems have shown strong potential for complex reasoning by coordinating specialized agents through structured communication. However, existing topology-evolution methods typically construct or optimize a collaboration topology for each query from scratch, leading to substantial online search overhead, high inference-time token consumption, and limited scalability in multi-domain settings. We propose TopoPrior, a framework for learning transferable topology priors for multi-agent LLM collaboration across domains. Rather than repeatedly searching for effective collaboration structures online, TopoPrior learns reusable topology priors from reference collaboration graphs collected offline from multiple domains and uses them to generate query-conditioned initial collaboration graphs for downstream refinement. By shifting part of topology search from per-query online optimization to offline prior learning, TopoPrior amortizes search cost while remaining compatible with existing topology-evolution backbones. Technically, TopoPrior contains two key components. First, a transferable topology prior learning module employs a conditional variational graph framework to capture reusable structural regularities across domains in a latent space. Second, a query-conditioned latent adaptation module introduces adversarial alignment to reduce unnecessary domain discrepancy while preserving query-relevant structural variation. Experiments on multi-domain reasoning benchmarks show that TopoPrior consistently improves several heterogeneous topology-evolution backbones while reducing online inference-time token usage, with only modest additional trainable parameters. These results suggest that transferable topology initialization is an effective and lightweight mechanism for improving the efficiency of multi-agent LLM collaboration across domains.