We report an experimental investigation on the effects of Ce-codoping in determining the radiation response of germanosilicate and phosphosilicate Optical Fibers (OFs) in the UV-Visible domain and up to doses of 1 MGy(SiO2). We show that the addition of Ce strongly impacts the Radiation Induced Attenuation (RIA) of both types of fibers. In the first case the radiation induced losses increase, whereas in the second one decrease. By combining the online RIA measurements with the Electron Paramagnetic Resonance (EPR) ones, we are able to infer the basic microscopic mechanisms taking place under irradiation, which involve the cerium codopant and some of the known Ge-related or P-related defects. More precisely, we found that part of the Ce atoms are incorporated in the glass matrix as Ce3+ ions by the production process and act as electron donor centers under irradiation. Consequently, the concentrations of radiation induced hole centers of Ge and P are drastically reduced. The reported results give an insight into possible ways of exploiting Ce codoping to control the radiation sensitivity of the OFs. Moreover, the OFs doped with cerium and phosphorous show a strongly reduced saturation effect at high radiation doses that make them a potential candidate for RIA-based dosimetry applications in a wide range of radiation doses.