A measurement of the ZZ production cross section in the ℓ−ℓ+ℓ′ −ℓ′+ and ℓ−ℓ+νν¯ 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 ZZ→ℓ−ℓ+νν¯ 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.