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Federated learning enables users to collaboratively train a machine learning model over their private datasets. Secure aggregation protocols are employed to mitigate information leakage about the local datasets from user-submitted model updates. This setup, however, still leaks the user participation in training, which can also be sensitive. Protecting user anonymity is even more challenging in dynamic environments where users may (re)join or leave the training process at any point of time. This paper introduces AnoFel, the first framework to support private and anonymous dynamic participation in federated learning (FL). AnoFel leverages several cryptographic primitives, the concept of anonymity sets, differential privacy, and a public bulletin board to support anonymous user registration, as well as unlinkable and confidential model update submission. Our system allows dynamic participation, where users can join or leave at any time without needing any recovery protocol or interaction. To assess security, we formalize a notion for privacy and anonymity in FL, and formally prove that AnoFel satisfies this notion. To the best of our knowledge, our system is the first solution with provable anonymity guarantees. To assess efficiency, we provide a concrete implementation of AnoFel, and conduct experiments showing its ability to support learning applications scaling to a large number of clients. For a TinyImageNet classification task with 512 clients, the client setup to join is less than 3 sec, and the client runtime for each training iteration takes a total of 8 sec, where the added overhead of AnoFel is 46% of the total runtime. We also compare our system with prior work and demonstrate its practicality. AnoFel client runtime is up to 5x faster than Truex et al., despite the added anonymity guarantee and dynamic user joining in AnoFel. Compared to Bonawitz et al., AnoFel is only 2x slower for added support for privacy in output, dynamic user joining, and anonymity.