Context. For Gaia DR2, 280 million spectra collected by the Radial Velocity Spectrometer instrument on board Gaia were processed, and median radial velocities were derived for 9.8 million sources brighter than GRVS = 12 mag. Aims: This paper describes the validation and properties of the median radial velocities published in Gaia DR2. Methods: Quality tests and filters were applied to select those of the 9.8 million radial velocities that have the quality to be published in Gaia DR2. The accuracy of the selected sample was assessed with respect to ground-based catalogues. Its precision was estimated using both ground-based catalogues and the distribution of the Gaia radial velocity uncertainties. Results: Gaia DR2 contains median radial velocities for 7 224 631 stars, with Teff in the range [3550, 6900] K, which successfully passed the quality tests. The published median radial velocities provide a full-sky coverage and are complete with respect to the astrometric data to within 77.2% (for G ≤ 12.5 mag). The median radial velocity residuals with respect to the ground-based surveys vary from one catalogue to another, but do not exceed a few 100 m s-1. In addition, the Gaia radial velocities show a positive trend as a function of magnitude, which starts around GRVS 9 mag and reaches about + 500 m s-1 at GRVS = 11.75 mag. The origin of the trend is under investigation, with the aim to correct for it in Gaia DR3. The overall precision, estimated from the median of the Gaia radial velocity uncertainties, is 1.05 km s-1. The radial velocity precision is a function of many parameters, in particular, the magnitude and effective temperature. For bright stars, GRVS ∈ [4, 8] mag, the precision, estimated using the full dataset, is in the range 220-350 m s-1, which is about three to five times more precise than the pre-launch specification of 1 km s-1. At the faint end, GRVS = 11.75 mag, the precisions for Teff = 5000 and 6500 K are 1.4 and 3.7 km s-1, respectively.