Sub-damped Lyman {alpha} systems (subDLAs; HI column densities of 19.0<=logN(HI)<20.3) are rarely included in the cosmic HI census performed at redshifts z_abs_>=1.5, yet are expected to contribute significantly to the overall HI mass budget of the Universe. In this paper, we present a blindly selected sample of 155 subDLAs found along 100 quasar sightlines (with a redshift path-length {Delta}X=475) in the XQ-100 legacy survey to investigate the contribution of subDLAs to the H I mass density of the Universe. The impact of X-Shooter's spectral resolution on Ly {alpha} absorber identification is evaluated, and found to be sufficient for reliably finding absorbers down to a column density of logN(HI)>=18.9. We compared the implications of searching for subDLAs solely using HI absorption versus the use of metal lines to confirm the identification, and found that metal-selection techniques would have missed 75 subDLAs. Using a bootstrap Monte Carlo simulation, we computed the column density distribution function (f(N, X)) and the cosmological H I mass density (Omega_HI_) of subDLAs and compared with our previous work based on the XQ-100 damped Lyman {alpha} systems. We do not find any significant redshift evolution in f(N, X) or Omega_HI_ for subDLAs. However, subDLAs contribute 10-20 per cent of the total Omega_HI_ measured at redshifts 2<z<5, and thus have a small but significant contribution to the HI budget of the Universe.