Clustered Federated Learning (CFL) is a novel framework for distributed multi-task learning under privacy constraints. It addresses the issue of suboptimal results in Federated Learning (FL) when local clients have divergent data distributions. CFL groups clients into clusters with jointly trainable data distributions, leveraging geometric properties of the FL loss surface. Unlike existing FL approaches, CFL does not require modifications to the communication protocol, works with non-convex objectives, and provides strong mathematical guarantees on clustering quality. It is flexible, privacy-preserving, and can handle varying client populations. CFL is a post-processing method that improves performance by allowing clients to arrive at more specialized models. The framework uses cosine similarity between gradient updates to infer clustering structure after FL has converged to a stationary point. Theoretical analysis and experiments on deep convolutional and recurrent neural networks on common FL datasets validate the effectiveness of CFL. The method is implemented without modifying the FL communication protocol and can be applied to non-convex objectives. The approach is demonstrated on MNIST and CIFAR-10 datasets with clients in different clusters, showing improved clustering accuracy and performance. The results indicate that CFL can effectively separate clients into clusters with congruent data distributions, leading to better model performance.Clustered Federated Learning (CFL) is a novel framework for distributed multi-task learning under privacy constraints. It addresses the issue of suboptimal results in Federated Learning (FL) when local clients have divergent data distributions. CFL groups clients into clusters with jointly trainable data distributions, leveraging geometric properties of the FL loss surface. Unlike existing FL approaches, CFL does not require modifications to the communication protocol, works with non-convex objectives, and provides strong mathematical guarantees on clustering quality. It is flexible, privacy-preserving, and can handle varying client populations. CFL is a post-processing method that improves performance by allowing clients to arrive at more specialized models. The framework uses cosine similarity between gradient updates to infer clustering structure after FL has converged to a stationary point. Theoretical analysis and experiments on deep convolutional and recurrent neural networks on common FL datasets validate the effectiveness of CFL. The method is implemented without modifying the FL communication protocol and can be applied to non-convex objectives. The approach is demonstrated on MNIST and CIFAR-10 datasets with clients in different clusters, showing improved clustering accuracy and performance. The results indicate that CFL can effectively separate clients into clusters with congruent data distributions, leading to better model performance.