Thermal camouflage has been successful in the conductive regime, where thermal metamaterials embedded in a conductive system can manipulate heat conduction inside the bulk. Most reported approaches are background-dependent and not applicable to radiative heat emitted from the surface of the system. A coating with engineered emissivity is one option for radiative camouflage, but only when the background has uniform temperature. Here, we propose a strategy for radiative camouflage of external objects on a given background using a structured thermal surface. The device is non-invasive and restores arbitrary background temperature distributions on its top. For many practical candidates of the background material with similar emissivity as the device, the object can thereby be radiatively concealed without a priori knowledge of the host conductivity and temperature. We expect this strategy to meet the demands of anti-detection and thermal radiation manipulation in complex unknown environments and to inspire developments in phononic and photonic thermotronics.