The results of modeling the conversion factor from rainfall-deposited unit activity of gamma-emitting radon and thoron daughter decay products to their created gamma-radiation dose rate as a function of height above the Earth’s surface using the Geant4 toolkit are presented in this paper. Thin layers of water, soil, and air, with the height of 0.1–10 mm, are considered as the source in order to examine whether the composition of the radiation source environment affects the simulation result. Cases with different absorber-atmosphere densities are simulated. The contribution of each radionuclide 212Bi, 214Bi, 212Pb, 214Pb and 208Tl to the total gamma background was determined. The dependence of dose rate growth during the precipitation period on the detector position in relation to the area covered by precipitation was investigated numerically. The obtained conversion factors are universal values, because do not depend on soil type (material) on which radionuclides are deposited by precipitation. These coefficients can be used for solving both direct tasks of radiation background recovery during precipitation and inverse tasks of determining the intensity and amount of precipitation by the known gamma background, as well as tasks to decipher the gamma background by the shape of the response to various phenomena. Also in this work, it is shown how thoron decay products can affect the response shape of gamma background on atmospheric precipitation.