A measurement of the ZZ production cross section in proton-proton collisions at √s = 7 TeV using data recorded by the ATLAS experiment at the Large Hadron Collider is presented. In a data sample corresponding to an integrated luminosity of 4.6 fb-1 collected in 2011, events are selected that are consistent either with two Z bosons decaying to electrons or muons or with one Z boson decaying to electrons or muons and a second Z boson decaying to neutrinos. The ZZ(*) → ℓ+ℓ-ℓ0+ℓ0- and ZZ → ℓ+ℓ-vv cross sections are measured in restricted phase-space regions. These results are then used to derive the total cross section for ZZ events produced with both Z bosons in the mass range 66 to 116 GeV, σ tot ZZ = 6.7 ± 0.7 (stat.) +0.4 -0.3 (syst.) ± 0.3 (lumi.) pb, which is consistent with the Standard Model prediction of 5.89+0.22 -0.18 pb calculated at next-to-leading order in QCD. The normalized differential cross sections in bins of various kinematic variables are presented. Finally, 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.