The production cross sections of top-quark pairs in association with massive vector bosons have been measured using data from pp collisions at √s = 8TeV. The dataset corresponds to an integrated luminosity of 20.3 fb-1 collected by the ATLAS detector in 2012 at the LHC. Final states with two, three or four leptons are considered. A fit to the data considering the t¯tW and t¯tZ processes simultaneously yields a significance of 5.0σ (4.2σ) over the background-only hypothesis for t¯tW (t¯tZ) production. The measured cross sections are t¯tW = 369+100 -91 fb and t¯tZ = 176+58 -52 fb. The background-only hypothesis with neither t¯tW nor t¯tZ production is excluded at 7.1σ. All measurements are consistent with next-to-leading-order calculations for the t¯tW and t¯tZ processes.