Measurements of the cross sections for top quark pairs produced in association with a W or Z boson are presented, using 8 TeV pp collision data corresponding to an integrated luminosity of 19.5 fb$^{−1}$, collected by the CMS experiment at the LHC. Final states are selected in which the associated W boson decays to a charged lepton and a neutrino or the Z boson decays to two charged leptons. Signal events are identified by matching reconstructed objects in the detector to specific final state particles from $ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $ or $ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $ decays. The $ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $ cross section is measured to be 382${− 102}^{+ 117}$ fb with a significance of 4.8 standard deviations from the background-only hypothesis. The $ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $ cross section is measured to be 242${− 55}^{+ 65}$ fb with a significance of 6.4 standard deviations from the background-only hypothesis. These measurements are used to set bounds on five anomalous dimension-six operators that would affect the $ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $ and $ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $ cross sections.