Volcanic ash clouds are a threat to air traffic security and, thus, can have significant societal and financial impact. Therefore, the detection and monitoring of volcanic ash clouds to enhance the safety of air traffic is of central importance. This work presents the development of the new retrieval algorithm VACOS (Volcanic Ash Cloud properties Obtained from SEVIRI) which is based on artificial neural networks, the thermal channels of the geostationary sensor MSG/SEVIRI and auxiliary data from a numerical weather prediction model. It derives a pixel classification as well as cloud top height, effective particle radius and, indirectly, the mass column concentration of volcanic ash clouds during day and night. A large set of realistic one-dimensional radiative transfer calculations for typical atmospheric conditions with and without generic volcanic ash clouds is performed to create the training dataset. The atmospheric states are derived from ECMWF data to cover the typical diurnal, annual and interannual variability. The dependence of the surface emissivity on surface type and viewing zenith angle is considered. An extensive dataset of volcanic ash optical properties is used, derived for a wide range of microphysical properties and refractive indices of various petrological compositions, including different silica contents and glass-to-crystal ratios; this constitutes a major innovation of this retrieval. The resulting ash-free radiative transfer calculations at a specific time compare well with corresponding SEVIRI measurements, considering the individual pixel deviations as well as the overall brightness temperature distributions. Atmospheric gas profiles and sea surface emissivities are reproduced with a high agreement, whereas cloudy cases can show large deviations on a single pixel basis (with 95th percentiles of the absolute deviations > 30 K), mostly due to different cloud properties in model and reality. Land surfaces lead to large deviations for both the single pixel comparison (with median absolute deviations > 3 K) and more importantly the brightness temperature distributions, most likely due to imprecise skin temperatures. The new method enables volcanic ash-related scientific investigations as well as aviation security-related applications.