The Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) is the first mission that will provide measurements from active profiling, passive imaging and a broadband radiometer from a single satellite platform. The passive multi-spectral imager (MSI) features four solar and three thermal infrared channels, and has a swath of 150 km and a spatial pixel resolution of 500 m. The MSI observations will provide across-track information on clouds and aerosol to extend the active profiling information into the swath. In this paper, we present the algorithm used for retrieving the cloud optical and physical products (M-COP), specifically cloud optical thickness, effective radius and top height. The algorithm is based on the solar and terrestrial MSI channels within an optimal estimation framework. This framework enables full error propagation given by the uncertainties in measurements and a priori information. The MSI cloud algorithm has been successfully exercised on different imagers and on synthetically generated MSI observations.