Estimating the depth of objects from a single image is a valuable task for many vision, robotics, and graphics applications. However, current methods often fail to produce accurate depth for objects in diverse scenes. In this work, we propose a simple yet effective Background Prompting strategy that adapts the input object image with a learned background. We learn the background prompts only using small scale synthetic object datasets. To infer object depth on a real image, we place the segmented object into the learned background prompt and run off-the-shelf depth networks. Background Prompting helps the depth networks focus on the foreground object, as they are made invariant to background variations. Moreover, Background Prompting minimizes the domain gap between synthetic and real object images, leading to better sim2real generalization than simple finetuning. Results on multiple synthetic and real datasets demonstrate consistent improvements in real object depths for a variety of existing depth networks.