The Z→ττ cross section is measured with the ATLAS experiment at the LHC in four different final states determined by the decay modes of the τ leptons: muon-hadron, electron-hadron, electron-muon, and muon-muon. The analysis is based on a data sample corresponding to an integrated luminosity of 36pb-1, at a proton-proton center-of-mass energy of √s=7TeV. Cross sections are measured separately for each final state in fiducial regions of high detector acceptance, as well as in the full phase space, over the mass region 66-116 GeV. The individual cross sections are combined and the product of the total Z production cross section and Z→ττ branching fraction is measured to be 0.97±0.07(stat)±0.06(syst)±0.03(lumi)nb, in agreement with next-to-next-to-leading order calculations.