The production cross sections of top-quark pairs in association with massive vector bosons have been measured using data from pp collisions at $$ \sqrt{s}=8 $$ 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 $$ t\overline{t}W $$ and $$ t\overline{t}Z $$ processes simultaneously yields a significance of 5.0σ (4.2σ) over the background-only hypothesis for $$ t\overline{t}W $$ ( $$ t\overline{t}Z $$ ) production. The measured cross sections are $$ {\sigma}_{t\overline{t}W}={369}_{-91}^{+100} $$ fb and $$ {\sigma}_{t\overline{t}Z}={176}_{-52}^{+58} $$ fb. The background-only hypothesis with neither $$ t\overline{t}W $$ nor $$ t\overline{t}Z $$ production is excluded at 7.1σ. All measurements are consistent with next-to-leading-order calculations for the $$ t\overline{t}W $$ and $$ t\overline{t}Z $$ processes.