The production cross sections of top-quark pairs in association with massive vector bosons have been measured using data from pp collisions at √s = 8 TeV. 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 t ¯ W and t t ¯ Z processes simultaneously yields a significance of 5.0 σ (4.2 σ ) over the background-only hypothesis for t t ¯ W ( t t ¯ Z ) production. The measured cross sections are σ t t ¯ W = 369 − 91 + 100 fb and σ t t ¯ Z = 176 − 52 + 58 fb. The background-only hypothesis with neither t t ¯ W production is excluded at 7.1 σ . All measurements are consistent with next-to-leading-order calculations for the t t ¯ W and t t ¯ Z processes.