We have obtained spectroscopic confirmation with Hubble Space Telescope WFC3/G141 of a first sizeable sample of nine quiescent galaxies at 2.4 < z < 3.3. Their average near-UV/optical rest-frame spectrum is characterized by low attenuation (AV ∼ 0.6 mag) and a strong Balmer break, larger than the 4000 Å break, corresponding to a fairly young age of ∼300 Myr. This formally classifies a substantial fraction of classically selected quiescent galaxies at z ∼ 3 as post-starbursts, marking their convergence to the quenching epoch. The rapid spectral evolution with respect to z ∼ 1.5 quiescent galaxies is not matched by an increase of residual star formation, as judged from the weak detection of [O ii]λ3727 emission, pointing to a flattening of the steep increase in gas fractions previously seen from z ∼ 0 to 1.8. However, radio 3 GHz stacked emission implies either much stronger dust-obscured star formation or substantial further evolution in radio-mode AGN activity with respect to z ∼ 1.5.