Lightweight compressed models are prevalent in Approximate Nearest Neighbor Search (ANNS) and Maximum Inner Product Search (MIPS) owing to their superiority of retrieval efficiency in large-scale datasets. However, results given by compressed methods are less accurate due to the curse of dimension and the limitations of optimization objectives (e.g., lacking interactions between queries and documents). Thus, we are encouraged to design a new learning algorithm for the compressed search index on high dimensions to improve retrieval performance. In this paper, we propose a novel KnowledgeDistillation for high dimensional search index framework (KDindex), with the aim of efficiently learning lightweight indexes by distilling knowledge from high-precision ANNS and MIPS models such as graph-based indexes. Specifically, the student is guided to keep the same ranking order of the top-k relevant results yielded by the teacher model, which acts as the additional supervision signals between queries and documents to learn the similarities between documents. Furthermore, to avoid the trivial solutions that all candidates are partitioned to the same centroid, the reconstruction loss that minimizes the compressed error, and the posting list balance strategy that equally allocates the candidates, are integrated into the learning objective. Experiment results demonstrate that KDindex outperforms existing learnable quantization-based indexes and is 40× lighter than the state-of-the-art non-exhaustive methods while achieving comparable recall quality.