Unsupervised domain adaptation (UDA) aims to mitigate the domain shift that occurs when transferring knowledge from a labeled source domain to an unlabeled target domain. While it has been studied for application in unsupervised person re-identification (ReID), the relations of feature distribution across the source and target domains remain underexplored, as they either ignore the local relations or omit the in-depth consideration of negative transfer when two domains do not share identical label spaces. In light of the above, this paper presents an innovative part-aware progressive adaptation network (PPAN) that exploits global and local relations for UDA-based ReID across domains. A multi-branch network is developed that explicitly learns discriminative feature representation from both whole-body images and body-part images under the supervision of a labeled source domain. Within each network branch, an independent UDA constraint is designed that aligns the global and local feature distributions from a labeled source domain with those of an unlabeled target domain. In addition, a novel progressive adaptation strategy (PAS) is designed that effectively alleviates the negative influence of outlier source identities. The proposed unsupervised ReID model is evaluated on five widely used datasets (Market-1501, DukeMTMC-reID, CUHK03, VIPeR and PRID), and experimental results demonstrate its superior robustness and effectiveness relative to state-of-the-art approaches.