The neutron time-of-flight facility n–TOF features a white neutron source produced by spallation through 20 GeV/c protons impinging on a lead target. The facility, aiming primarily at the measurement of neutron-induced reaction cross sections, was operating at CERN between 2001 and 2004, and then underwent a major upgrade in 2008. This paper presents in detail all the characteristics of the new neutron beam in the currently available configurations, which correspond to two different collimation systems and two choices of neutron moderator. The characteristics discussed include the intensity and energy dependence of the neutron flux, the spatial profile of the beam, the in-beam background components and the energy resolution/broadening. The discussion of these features is based on dedicated measurements and Monte Carlo simulations, and includes estimations of the systematic uncertainties of the mentioned quantities.