We present a novel end-to-end reinforcement learning approach to automatic taxonomy induction from a set of terms. While prior methods treat the problem as a two-phase task (i.e., detecting hypernymy pairs followed by organizing these pairs into a tree-structured hierarchy), we argue that such two-phase methods may suffer from error propagation, and cannot effectively optimize metrics that capture the holistic structure of a taxonomy. In our approach, the representations of term pairs are learned using multiple sources of information and used to determine which term to select and where to place it on the taxonomy via a policy network. All components are trained in an end-to-end manner with cumulative rewards, measured by a holistic tree metric over the training taxonomies. Experiments on two public datasets of different domains show that our approach outperforms prior state-of-the-art taxonomy induction methods up to 19.6% on ancestor F1.