Galaxies, forming and evolving within their host dark matter haloes, are the end-product of a balance between gas cooling, star formation and feedback. Energy/Momentum feedback, in particular from active galactic nuclei (AGN), is believed to play a crucial role in the evolution of galaxies by gradually quenching their star formation. In the local Universe many galaxies with an AGN are indeed observed to reside in the so-called green valley, usually interpreted as a transition phase from a blue star formation epoch to a red quenched state. We use data from the Sloan Digital Sky Survey to show that such an interpretation requires substantial revision. Optically-selected nearby AGN galaxies follow exponentially declining star formation histories, as normal galaxies of similar stellar and dark matter halo mass, reaching in the recent past (~0.1 Gyr ago) star formation rate levels consistent with a quiescent population. However, we find that local AGN galaxies have experienced a sudden increase in their star formation rate, unfolding on timescales similar to those typical of AGN activity, suggesting that both star formation and AGN activity were triggered simultaneously. We find that this quenching process followed by an enhancement in the star formation rate is common to AGN galaxies and more pronounced in early type galaxies. Our results demonstrate that local AGN galaxies are not a transition type between star-forming and quiescent galaxies as previously postulated, but simply galaxies experiencing a recent gas accretion episode.