Structured and grounded representation of text is typically formalized by closed information extraction, the problem of extracting an exhaustive set of (subject, relation, object) triplets that are consistent with a predefined set of entities and relations from a knowledge base schema. Most existing works are pipelines prone to error accumulation, and all approaches are only applicable to unrealistically small numbers of entities and relations. We introduce GenIE (generative information extraction), the first end-to-end autoregressive formulation of closed information extraction. GenIE naturally exploits the language knowledge from the pre-trained transformer by autoregressively generating relations and entities in textual form. Thanks to a new bi-level constrained generation strategy, only triplets consistent with the predefined knowledge base schema are produced. Our experiments show that GenIE is state-of-the-art on closed information extraction, generalizes from fewer training data points than baselines, and scales to a previously unmanageable number of entities and relations. With this work, closed information extraction becomes practical in realistic scenarios, providing new opportunities for downstream tasks. Finally, this work paves the way towards a unified end-to-end approach to the core tasks of information extraction. Code, data and models available at https://github.com/epfl-dlab/GenIE.