A measurement of the ZZ production cross section in the ℓ − ℓ + ℓ ′ − ℓ ′ + and ℓ − ℓ + ν ν ¯ channels (ℓ = e, μ ) in proton-proton collisions at √s = 8 TeV at the Large Hadron Collider at CERN, using data corresponding to an integrated luminosity of 20.3 fb −1 collected by the ATLAS experiment in 2012 is presented. The fiducial cross sections for ZZ → ℓ − ℓ + ℓ ′ − ℓ ′ + and Z Z → ℓ − ℓ + ν ν ¯ are measured in selected phase-space regions. The total cross section for ZZ events produced with both Z bosons in the mass range 66 to 116 GeV is measured from the combination of the two channels to be 7.3 ± 0.4(stat) ± 0.3(syst) − 0.1 − 0.2 (lumi) pb, which is consistent with the Standard Model prediction of 6. 6 − 0.6 + 0.7 pb. The differential cross sections in bins of various kinematic variables are presented. The differential event yield as a function of the transverse momentum of the leading Z boson is used to set limits on anomalous neutral triple gauge boson couplings in ZZ production.