Context. The characterisation of Earth-size exoplanets through transit photometry has stimulated new generations of high-precision instruments. In that respect, the Characterising Exoplanet Satellite (CHEOPS) is designed to perform photometric observations of bright stars to obtain precise radii measurements of transiting planets. The CHEOPS instrument will have the capability to follow up bright hosts provided by radial-velocity facilities. With the recent launch of the Transiting Exoplanet Survey Satellite (TESS), CHEOPS may also be able to confirm some of the long-period TESS candidates and to improve the radii precision of confirmed exoplanets. Aims. The high-precision photometry of CHEOPS relies on careful on-ground calibration of its payload. For that purpose, intensive pre-launch campaigns of measurements were carried out to calibrate the instrument and characterise its photometric performances. This work reports on the main results of these campaigns. It provides a complete analysis of data sets and estimates in-flight photometric performance by means of an end-to-end simulation. Instrumental systematics were measured by carrying out long-term calibration sequences. Using an end-to end model, we simulated transit observations to evaluate the impact of in-orbit behaviour of the satellite and to determine the achievable precision on the planetary radii measurement. Methods. After introducing key results from the payload calibration, we focussed on the data analysis of a series of long-term measurements of uniformly illuminated images. The recorded frames were corrected for instrumental effects and a mean photometric signal was computed on each image. The resulting light curve was corrected for systematics related to laboratory temperature fluctuations. Transit observations were simulated, considering the payload performance parameters. The data were corrected using calibration results and estimates of the background level and position of the stellar image. The light curve was extracted using aperture photometry and analysed with a transit model using a Markov chain Monte Carlo algorithm. Results. In our analysis, we show that the calibration test set-up induces thermally correlated features in the data that can be corrected in post-processing to improve the quality of the light curves. We find that on-ground photometric performances of the instrument measured after this correction is of the order of 15 parts per million over five hours. Using our end-to-end simulation, we determine that measurements of planet-to-star radii ratio with a precision of 2% for a Neptune-size planet transiting a K-dwarf star and 5% for an Earth-size planet orbiting a Sun-like star are possible with CHEOPS. These values correspond to transit depths obtained with signal-to-noise ratios of 25 and 10, respectively, allowing the characterisation and detection of these planets. The pre-launch CHEOPS performances are shown to be compliant with the mission requirements.