In software development, it is common for programmers to copy-paste or port code snippets and then adapt them to their use case. This scenario motivates the code adaptation task – a variant of program repair which aims to adapt variable identifiers in a pasted snippet of code to the surrounding, preexisting context. However, no existing approach has been shown to effectively address this task. In this paper, we introduce AdaptivePaste, a learning-based approach to source code adaptation, based on transformers and a dedicated dataflow-aware deobfuscation pre-training task to learn meaningful representations of variable usage patterns. We demonstrate that AdaptivePaste can learn to adapt Python source code snippets with 67.8% exact match accuracy. We study the impact of confidence thresholds on the model predictions, showing the model precision can be further improved to 85.9% with our parallel-decoder transformer model in a selective code adaptation setting. To assess the practical use of AdaptivePaste we perform a user study among Python software developers on real-world copy-paste instances. The results show that AdaptivePaste reduces dwell time to nearly half the time it takes to port code manually, and helps to avoid bugs. In addition, we utilize the participant feedback to identify potential avenues for improvement.