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The problem of generalizing deep neural networks from multiple source domains to a target one is studied under two settings: When unlabeled target data is available, it is a multi-source unsupervised domain adaptation (UDA) problem, otherwise a domain generalization (DG) problem. We propose a unified framework termed domain adaptive ensemble learning (DAEL) to address both problems. A DAEL model is composed of a CNN feature extractor shared across domains and multiple classifier heads each trained to specialize in a particular source domain. Each such classifier is an expert to its own domain and a non-expert to others. DAEL aims to learn these experts collaboratively so that when forming an ensemble, they can leverage complementary information from each other to be more effective for an unseen target domain. To this end, each source domain is used in turn as a pseudo-target-domain with its own expert providing supervisory signal to the ensemble of non-experts learned from the other sources. For unlabeled target data under the UDA setting where real expert does not exist, DAEL uses pseudo-label to supervise the ensemble learning. Extensive experiments on three multi-source UDA datasets and two DG datasets show that DAEL improves the state of the art on both problems, often by significant margins. The code is released at \url{https://github.com/KaiyangZhou/Dassl.pytorch}.