Modern entity linking systems rely on large collections of documents specifically annotated for the task (e.g., AIDA CoNLL). In contrast, we propose an approach which exploits only naturally occurring information: unlabeled documents and Wikipedia. Our approach consists of two stages. First, we construct a high recall list of candidate entities for each mention in an unlabeled document. Second, we use the candidate lists as weak supervision to constrain our document-level entity linking model. The model treats entities as latent variables and, when estimated on a collection of unlabelled texts, learns to choose entities relying both on local context of each mention and on coherence with other entities in the document. The resulting approach rivals fully-supervised state-of-the-art systems on standard test sets. It also approaches their performance in the very challenging setting: when tested on a test set sampled from the data used to estimate the supervised systems. By comparing to Wikipedia-only training of our model, we demonstrate that modeling unlabeled documents is beneficial.