Entity resolution (ER) (record linkage or de-duplication) is the process of merging together noisy databases, often in the absence of a unique identifier. A major advancement in ER methodology has been the application of Bayesian generative models. Such models provide a natural framework for clustering records to unobserved (latent) entities, while providing exact uncertainty quantification and tight performance bounds. Despite these advancements, existing models do not scale to realistically-sized databases (larger than 1000 records) and they do not incorporate probabilistic blocking. In this paper, we propose "distributed Bayesian linkage" or d-blink -- the first scalable and distributed end-to-end Bayesian model for ER, which propagates uncertainty in blocking, matching and merging. We make several novel contributions, including: (i) incorporating probabilistic blocking directly into the model through auxiliary partitions; (ii) support for missing values; (iii) a partially-collapsed Gibbs sampler; and (iv) a novel perturbation sampling algorithm (leveraging the Vose-Alias method) that enables fast updates of the entity attributes. Finally, we conduct experiments on five data sets which show that d-blink can achieve significant efficiency gains -- in excess of 300$\times$ -- when compared to existing non-distributed methods.