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Multi-source entity linkage focuses on integrating knowledge from multiple sources by linking the records that represent the same real world entity. This is critical in high-impact applications such as data cleaning and user stitching. The state-of-the-art entity linkage pipelines mainly depend on supervised learning that requires abundant amounts of training data. However, collecting well-labeled training data becomes expensive when the data from many sources arrives incrementally over time. Moreover, the trained models can easily overfit to specific data sources, and thus fail to generalize to new sources due to significant differences in data and label distributions. To address these challenges, we present AdaMEL, a deep transfer learning framework that learns generic high-level knowledge to perform multi-source entity linkage. AdaMEL models the attribute importance that is used to match entities through an attribute-level self-attention mechanism, and leverages the massive unlabeled data from new data sources through domain adaptation to make it generic and data-source agnostic. In addition, AdaMEL is capable of incorporating an additional set of labeled data to more accurately integrate data sources with different attribute importance. Extensive experiments show that our framework achieves state-of-the-art results with 8.21% improvement on average over methods based on supervised learning. Besides, it is more stable in handling different sets of data sources in less runtime.