We present Magic Insert, a method to drag-and-drop subjects from a user-provided image into a target image of a different style in a plausible manner while matching the style of the target image. This work formalizes our version of the problem of style-aware drag-and-drop and proposes to tackle it by decomposing it into two sub-problems: style-aware personalization and realistic object insertion in stylized images. For style-aware personalization, we cast our method as a weight-and-text-embedding finetuning method with inference-time module-targeted style injection. For subject insertion, we propose Bootstrapped Domain Adaption (BDA) to adapt a domain-specific photorealistic object insertion model to the domain of diverse artistic styles. Overall, the method significantly outperforms traditional and state-of-the-art approaches that struggle with quality, subject fidelity and harmonious stylization. Finally, we present a new dataset, SubjectPlop, to facilitate evaluation and future progress in this area.