The Tropospheric Monitoring Instrument (TROPOMI) spectrometer is the single payload of the Copernicus Sentinel 5 Precursor (S5P) mission. It measures Earth radiance spectra in the shortwave infrared spectral range around 2.3 μm with a dedicated instrument module. These measurements provide carbon monoxide (CO) total column densities over land, which for clear sky conditions are highly sensitive to the tropospheric boundary layer. For cloudy atmospheres over land and ocean, the column sensitivity changes according to the light path through the atmosphere. In this study, we present the physics-based operational S5P algorithm to infer atmospheric CO columns satisfying the envisaged accuracy ( < 15%) and precision (< 10%) both for clear sky and cloudy observations with low cloud height. Here, methane absorption in the 2.3 μm range is combined with methane abundances from a global chemical transport model to infer information on atmospheric scattering. For efficient processing, we deploy a linearized two-stream radiative transfer model as forward model and a profile scaling approach to adjust the CO abundance in the inversion. Based on generic measurement ensembles, including clear sky and cloudy observations, we estimated the CO retrieval precision to be ≤ 11% for surface albedo ≥ 0.03 and solar zenith angle ≤ 70°. CO biases of ≤ 3% are introduced by inaccuracies in the methane a priori knowledge. For strongly enhanced CO concentrations in the tropospheric boundary layer and for cloudy conditions, CO errors in the order of 8% can be introduced by the retrieval of cloud parameters of our algorithm. Moreover, we estimated the effect of a distorted spectral instrument response due to the inhomogeneous illumination of the instrument entrance slit in the flight direction to be < 2 % with pseudo-random characteristics when averaging over space and time. Finally, the CO data exploitation is demonstrated for a TROPOMI orbit of simulated shortwave infrared measurements. Overall, the study demonstrates that for an instrument that performs in compliance with the pre-flight specifications, the CO product will meet the required product performance well.