We present a physical model to calculate cosmic ray induced ionization in the atmosphere. The model is based on the Monte Carlo CORSIKA tool, which simulates full development of an electromagnetic-muon-nucleonic cascade in the atmosphere, with the FLUKA package used for low-energy interactions. The direct ionization by primary cosmic rays is explicitly taken into account. The model is applicable to the entire atmosphere, from the ground up to the stratosphere. A comparison to fragmentary direct measurements of the ionization in the atmosphere confirms the validity of the model in the whole range of geographical latitudes and altitudes. Results of the full Monte Carlo simulation are tabulated in a form of the ionization yield function. These tables are given together with a detailed recipe, which allows a user to compute easily the cosmic ray induced ionization for given location, altitude and the spectrum of cosmic rays. This provides a new tool for a quantitative study of the space weather influence upon the Earth's environment. Some practical applications are discussed.