We describe the execution and data reduction of the European Southern Observatory Large Programme "Quasars and their absorption lines: a legacy survey of the high-redshift universe with VLT/XSHOOTER" (hereafter `XQ-100'). XQ-100 has produced and made publicly available an homogeneous and high-quality sample of echelle spectra of 100 QSOs at redshifts z~3.5-4.5 observed with full spectral coverage from 315 to 2500 nm at a resolving power ranging from R~4000 to 7000, depending on wavelength. The median signal-to-noise ratios are 33, 25 and 43, as measured at rest-frame wavelengths 1700, 3000 and 3600 Angstrom, respectively. This paper provides future users of XQ-100 data with the basic statistics of the survey, along with details of target selection, data acquisition and data reduction. The paper accompanies the public release of all data products, including 100 reduced spectra. XQ-100 is the largest spectroscopic survey to date of high-redshift QSOs with simultaneous rest-frame UV/optical coverage, and as such enables a wide range of extragalactic research, from cosmology and galaxy evolution to AGN astrophysics.