A new full model of the atmospheric transport of cosmogenic $^{10}$Be is presented based on the specialized SOCOL‐AERv2‐BE chemistry‐climate model coupled with the CRAC:10Be isotope production model. The model includes all the relevant atmospheric processes and allows computing the isotope concentration at any given location and time. The full model is directly compared with $^{10}$Be isotope measurements in five Antarctic and Greenland ice cores for the period 1980–2007. The model reasonably well reproduces the average concentration and solar‐cycle dependency or the lack of it for most observational sites but does not perfectly catch the interannual variability at sites with complex orography likely due to the coarse model grid. This implies that the model correctly reproduces the large‐scale atmospheric dynamics but effectively averages out synoptic‐scale variability. It is found that the dominant source of 10 Be is located in the middle stratosphere (25–40 km), in the tropical (<30° latitudes) and polar (>60°) regions, as produced by galactic cosmic rays and solar energetic particles, respectively. It is shown that >60% (90%) of $^{10}$Be produced in the atmosphere reaches the Earth's surface within one (two) years, respectively. For practical purposes, a simple parameterization of the full‐model results is presented which agrees with the full model within 20% in polar regions. This parameterization allows one to make a quick estimate of near‐ground 10 Be concentrations based only on production rates without heavy calculations. This practical approach can be applied to studies of solar and geomagnetic variability using cosmogenic isotopes.