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Deep learning has been successful for many computer vision tasks due to the availability of shared and centralised large-scale training data. However, increasing awareness of privacy concerns poses new challenges to deep learning, especially for human subject related recognition such as person re-identification (Re-ID). In this work, we solve the Re-ID problem by decentralised learning from non-shared private training data distributed at multiple user sites of independent multi-domain label spaces. We propose a novel paradigm called Federated Person Re-Identification (FedReID) to construct a generalisable global model (a central server) by simultaneously learning with multiple privacy-preserved local models (local clients). Specifically, each local client receives global model updates from the server and trains a local model using its local data independent from all the other clients. Then, the central server aggregates transferrable local model updates to construct a generalisable global feature embedding model without accessing local data so to preserve local privacy. This client-server collaborative learning process is iteratively performed under privacy control, enabling FedReID to realise decentralised learning without sharing distributed data nor collecting any centralised data. Extensive experiments on ten Re-ID benchmarks show that FedReID achieves compelling generalisation performance beyond any locally trained models without using shared training data, whilst inherently protects the privacy of each local client. This is uniquely advantageous over contemporary Re-ID methods.