Feedback, in particular from active galactic nuclei (AGNs), is believed to play a crucial role in the evolution of galaxies. 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-forming 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 time-scales similar to those typical of AGN activity, suggesting that both star formation and AGN activity were triggered simultaneously. We find that this quenching 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 just a simple transition type between star-forming and quiescent galaxies as previously postulated.