Listwise reranking with Large Language Models (LLMs) has emerged as the state-of-the-art approach, consistently establishing new performance benchmarks in passage reranking. However, their practical application faces two critical hurdles: the prohibitive computational overhead and high latency of processing long token sequences, and the performance degradation caused by phenomena like "lost in the middle" in long contexts. To address these challenges, we introduce Compress-then-Rank (C2R), an efficient framework that performs listwise reranking not on original passages, but on their compact multi-vector surrogates. These surrogates can be pre-computed and cached for all passages in the corpus. The effectiveness of C2R hinges on three key innovations. First, the compressor model is pre-trained on a combination of text restoration and continuation objectives, enabling high-fidelity compressed vector sequences that mitigate the semantic loss common in single-vector methods. Second, a novel input scheme prepends embeddings of each ordinal index (e.g., 1:) to its corresponding compressed vector sequence, which both delineates passage boundaries and guides the reranker LLM to generate a ranked list. Finally, the compressor and reranker are jointly optimized, making the compression explicitly ranking-aware for the ranking objective. Extensive experiments on major reranking benchmarks demonstrate that C2R provides substantial speedups while achieving competitive and even superior ranking performance compared to full-text reranking methods. The related code is provided in the supplementary materials.