From the VIMOS VLT Deep Survey (VVDS), we select a sample of 16 galaxies with spectra which identify them as having recently undergone a strong starburst and subsequent fast quenching of star formation. These post-starburst galaxies lie in the redshift range 0.5 < z < 1.0 with masses >109.75 M⊙. They have a number density of 1 × 10−4 Mpc−3, almost two orders of magnitude sparser than the full galaxy population with the same mass limit. We compare with simulations to show that the galaxies are consistent with being the descendants of gas-rich major mergers. Starburst mass fractions must be larger than ∼5–10 per cent and decay times shorter than ∼108 yr for post-starburst (PSB) spectral signatures to be observed in the simulations. We find that the presence of black hole feedback does not greatly affect the evolution of the simulated merger remnants through the PSB phase. The multiwavelength spectral energy distributions of the PSB galaxies show that 5/16 have completely ceased the formation of new stars. These five galaxies correspond to a mass flux entering the red-sequence of , assuming the defining spectroscopic features are detectable for 0.35 Gyr. If the galaxies subsequently remain on the red sequence, this accounts for 38+4−11 per cent of the growth rate of the red sequence. Finally, we compare our high-redshift results with a sample of galaxies with 0.05 < z < 0.1 observed in the Sloan Digital Sky Survey and United Kingdom Infrared Telescope Infrared Deep Survey. We find a very strong redshift evolution: the mass density of strong PSB galaxies is 230 times lower at z∼ 0.07 than at z∼ 0.7.