The construction of the Tycho-2 Catalogue is described. The catalogue contains astrometric positions and proper motions as well as two-colour photometric data for 2.5 million stars. The Tycho-2 positions and magnitudes are based on precisely the same observations as the original Tycho Catalogue (hereafter Tycho-1) collected by the sky mapper of the ESA Hipparcos satellite, but Tycho-2 is much bigger and slightly more precise, owing to a more advanced reduction technique. Components of double stars with separations down to 0.8 arcsec are included. Proper motions precise to about 2.5 mas/yr are given as derived from a comparison with the Astrographic Catalogue and 143 other astrometric catalogues, all reduced to the Hipparcos celestial coordinate system. Tycho-2 supersedes in most applications Tycho-1, and the ACT and TRC catalogues based on Tycho-1.