We propose a general and efficient framework to control auto-regressive generation models with NeurAlly-Decomposed Oracle (NADO). Given a pre-trained base language model and a sequence-level boolean oracle function, we aim to decompose the oracle function into token-level guidance to steer the base model in text generation. Specifically, the token-level guidance is provided by NADO, a neural model trained with examples sampled from the base model, demanding no additional auxiliary labeled data. Based on posterior regularization, we present the close-form optimal solution to incorporate the decomposed token-level guidance into the base model for controllable generation. We further discuss how the neural approximation affects the quality of the solution. These experiments conducted on two different applications: (1) text generation with lexical constraints and (2) machine translation with formality control demonstrate that our framework efficiently guides the base model towards the given oracle while keeping high generation quality.