This study presents the map of the external effective annual dose rate (1:200,000 scale) due to terrestrial and cosmic radiation. The terrestrial dose is assessed via gamma ray spectroscopy combining radiometric data from airborne surveys and laboratory measurements. The geostatistical method Collocated CoKriging is used for the spatial interpolation of the sparse gamma ray data, adopting a high-resolution geological map as ancillary information. The obtained numerical map is integrated with the cosmic radiation effective dose rate calculated using the CARI-7 software tool that considers the effects of altitude, latitude, and the solar magnetic activity cycle. The absorbed dose rate due to radioactivity of the main lithological groups is studied and, for the most populated municipalities, the population-weighted average effective dose is also calculated. For future generations, this map will be a reference tool for evaluating radiological effects in case of accidental events like radioactive fallout or environmental contaminations.