Satellite image composition plays a critical role in remote sensing applications such as data augmentation, disaste simulation, and urban planning. We propose HarmoniDiff-RS, a training-free diffusion-based framework for harmonizing composite satellite images under diverse domain conditions. Our method aligns the source and target domains through a Latent Mean Shift operation that transfers radiometric characteristics between them. To balance harmonization and content preservation, we introduce a Timestep-wise Latent Fusion strategy by leveraging early inverted latents for high harmonization and late latents for semantic consistency to generate a set of composite candidates. A lightweight harmony classifier is trained to further automatically select the most coherent result among them. We also construct RSIC-H, a benchmark dataset for satellite image harmonization derived from fMoW, providing 500 paired composition samples. Experiments demonstrate that our method effectively performs satellite image composition, showing strong potential for scalable remote-sensing synthesis and simulation tasks. Code is available at: https://github.com/XiaoqiZhuang/HarmoniDiff-RS.