This catalogue provides distances estimates (and uncertainties therein) for 1.33 billion stars over the whole sky brighter than about G=20.7. These have been estimated using the parallaxes (and their uncertainties) from Gaia DR2. A Bayesian procedure was used involving a prior with a single parameter L(l,b), which varies smoothly with Galactic longitude and latitude according to a Galaxy model. The posterior is summarized with a point estimate (usually the mode) and a confidence interval (usually the 68% highest density interval). The estimation procedure is described in detail in the accompanying paper, which also analyses the catalogue content.