Combining the precise parallaxes and optical photometry delivered by Gaia's second data release (DR2) with the photometric catalogues of Pan-STARRS1, 2MASS, and AllWISE, we compute Bayesian distances, extinctions, and stellar parameters (effective temperatures, gravities, metallicities, and masses) for stars brighter than G=18. Because of the wide wavelength range used, our results substantially improve the accuracy and precision of the Gaia DPAC results using Gaia DR2 alone. We achieve a median precision of 6% in distance and 0.17 mag in V-band extinction at G=14, degrading towards fainter magnitudes (15% and 0.20 mag at G=16; 30% and 0.25 mag at G=17). The results are carefully evaluated and flagged, and will be released through the ADQL query interface of the Gaia mirror at AIP (gaia.aip.de), and temporarily as binary tables. As first applications, we provide extinction maps as a function of distance, distance- and extinction-corrected colour-magnitude diagrams, and extensive kinematic maps of the Galaxy. Our results also serve to assess targeting strategies of the future 4MOST spectroscopic surveys. The produced catalogue may potentially be of interest for a number of existing and future projects within the institute.