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Domain generalization (DG) offers a preferable real-world setting for Person Re-Identification (Re-ID), which trains a model using multiple source domain datasets and expects it to perform well in an unseen target domain without any model updating. Unfortunately, most DG approaches are designed explicitly for classification tasks, which fundamentally differs from the retrieval task Re-ID. Moreover, existing applications of DG in Re-ID cannot correctly handle the massive variation among Re-ID datasets. In this paper, we identify two fundamental challenges in DG for Person Re-ID: domain-wise variations and identity-wise similarities. To this end, we propose an end-to-end Dual Distribution Alignment Network (DDAN) to learn domain-invariant features with dual-level constraints: the domain-wise adversarial feature learning and the identity-wise similarity enhancement. These constraints effectively reduce the domain-shift among multiple source domains further while agreeing to real-world scenarios. We evaluate our method in a large-scale DG Re-ID benchmark and compare it with various cutting-edge DG approaches. Quantitative results show that DDAN achieves state-of-the-art performance.