Bregman distances (also known as Bregman divergences) are widely used in machine learning, speech recognition and signal processing, and kNN searches with Bregman distances have become increasingly important with the rapid advances of multimedia applications. Data in multimedia applications such as images and videos are commonly transformed into space of hundreds of dimensions. Such high-dimensional space has posed significant challenges for existing kNN search algorithms with Bregman distances, which could only handle data of medium dimensionality (typically less than 100). This paper addresses the urgent problem of high-dimensional kNN search with Bregman distances. We propose a novel partition-filter-refinement framework. Specifically, we propose an optimized dimensionality partitioning scheme to solve several non-trivial issues. First, an effective bound from each partitioned subspace to obtain exact kNN results is derived. Second, we conduct an in-depth analysis of the optimized number of partitions and devise an effective strategy for partitioning. Third, we design an efficient integrated index structure for all the subspaces together to accelerate the search processing. Moreover, we extend our exact solution to an approximate version by a trade-off between the accuracy and efficiency. Experimental results on four real-world datasets and two synthetic datasets show the clear advantage of our method in comparison to state-of-the-art algorithms.