Reranking documents based on their relevance to a given query is critical in information retrieval. Traditional reranking methods often focus on improving the initial rankings but lack transparency, failing to explain why one document is ranked higher. In this paper, we introduce ReasoningRank, a novel reranking approach that enhances clarity by generating two types of reasoning: explicit reasoning, which explains how a document addresses the query, and comparison reasoning, which justifies the relevance of one document over another. We leverage large language models (LLMs) as teacher models to generate these explanations and distill this knowledge into smaller, more resource-efficient student models. While the student models may not outperform LLMs in speed, they significantly reduce the computational burden by requiring fewer resources, making them more suitable for large-scale or resource-constrained settings. These student models are trained to both generate meaningful reasoning and rerank documents, achieving competitive performance across multiple datasets, including MSMARCO and BRIGHT. Experiments demonstrate that ReasoningRank improves reranking accuracy and provides valuable insights into the decision-making process, offering a structured and interpretable solution for reranking tasks.