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 >10^9.75Msun. They have a number density of 1x10^-4 per 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% and decay times shorter than ~10^8 years for post-starburst 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 post-starburst phase. The multiwavelength spectral energy distributions of the post-starburst galaxies show that 5/16 have completely ceased the formation of new stars. These 5 galaxies correspond to a mass flux entering the red-sequence of rhodot(A->Q, PSB) = 0.0038Msun/Mpc^3/yr, assuming the defining spectroscopic features are detectable for 0.35Gyr. If the galaxies subsequently remain on the red sequence, this accounts for 38(+4/-11)% 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 SDSS and UKIDSS surveys. We find a very strong redshift evolution: the mass density of strong post-starburst galaxies is 230 times lower at z~0.07 than at z~0.7.
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