Automated storytelling has long captured the attention of researchers for the ubiquity of narratives in everyday life. However, it is challenging to maintain coherence and stay on-topic toward a specific ending when generating narratives with neural language models. In this paper, we introduce Story generation with Reader Models (StoRM), a framework in which a reader model is used to reason about the story should progress. A reader model infers what a human reader believes about the concepts, entities, and relations about the fictional story world. We show how an explicit reader model represented as a knowledge graph affords story coherence and provides controllability in the form of achieving a given story world state goal. Experiments show that our model produces significantly more coherent and on-topic stories, outperforming baselines in dimensions including plot plausibility and staying on topic. Our system also outperforms outline-guided story generation baselines in composing given concepts without ordering.