We present the MUSE Hubble Ultra Deep Survey, a mosaic of nine MUSE fields covering 90% of the entire HUDF region with a 10-h deep exposure time, plus a deeper 31-h exposure in a single 1.15 arcmin2 field. The improved observing strategy and advanced data reduction results in datacubes with sub-arcsecond spatial resolution (0.̋65 at 7000 Å) and accurate astrometry (0.̋07 rms). We compare the broadband photometric properties of the datacubes to HST photometry, finding a good agreement in zeropoint up to mAB = 28 but with an increasing scatter for faint objects. We have investigated the noise properties and developed an empirical way to account for the impact of the correlation introduced by the 3D drizzle interpolation. The achieved 3σ emiss...