Using combined asteroseismic and spectroscopic observations of 418 red-giant stars close to the Galactic disc plane ( 6 kpc < R _ { Gal } \lesssim 13 kpc , |Z _ { Gal } | < 0.3 kpc ) , we measure the age dependence of the radial metallicity distribution in the Milky Way ’ s thin disc over cosmic time . The slope of the radial iron gradient of the young red-giant population ( -0.058 \pm 0.008 [ stat . ] \pm 0.003 [ syst . ] dex/kpc ) is consistent with recent Cepheid measurements . For stellar populations with ages of 1 - 4 Gyr the gradient is slightly steeper , at a value of -0.066 \pm 0.007 \pm 0.002 dex/kpc , and then flattens again to reach a value of \sim - 0.03 dex/kpc for stars with ages between 6 and 10 Gyr . Our results are in good agreement with a state-of-the-art chemo-dynamical Milky-Way model in which the evolution of the abundance gradient and its scatter can be entirely explained by a non-varying negative metallicity gradient in the interstellar medium , together with stellar radial heating and migration . We also offer an explanation for why intermediate-age open clusters in the Solar Neighbourhood can be more metal-rich , and why their radial metallicity gradient seems to be much steeper than that of the youngest clusters . Already within 2 Gyr , radial mixing can bring metal-rich clusters from the innermost regions of the disc to Galactocentric radii of 5 to 8 kpc . We suggest that these outward-migrating clusters may be less prone to tidal disruption and therefore steepen the local intermediate-age cluster metallicity gradient . Our scenario also explains why the strong steepening of the local iron gradient with age is not seen in field stars . In the near future , asteroseismic data from the K2 mission will allow for improved statistics and a better coverage of the inner-disc regions , thereby providing tighter constraints on the evolution of the central parts of the Milky Way .