Modern language models have the capacity to store and use immense amounts of knowledge about real-world entities, but it remains unclear how to update such knowledge stored in model parameters. While prior methods for updating knowledge in LMs successfully inject atomic facts, updated LMs fail to make inferences based on injected facts. In this work, we demonstrate that a context distillation-based approach can both impart knowledge about entities \emph{and} propagate that knowledge to enable broader inferences. Our approach consists of two stages: transfer set generation and distillation on the transfer set. We first generate a transfer set by prompting a language model to generate continuations from the entity definition. Then, we update the model parameters so that the distribution of the LM (the 'student') matches the distribution of the LM conditioned on the definition (the 'teacher') on the transfer set. Our experiments demonstrate that this approach is more effective at propagating knowledge updates than fine-tuning and other gradient-based knowledge-editing methods. Moreover, it does not compromise performance in other contexts, even when injecting the definitions of up to 150 entities at once.