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 − ℓ ′+ ℓ ′− and ZZ→ℓ+ℓ−νν¯¯ 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, σtotZZ=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.