First measurements of the W → ℓν and Z/γ* → ℓℓ (ℓ = e; μ) production cross sections in proton-proton collisions at √s = 7TeV are presented using data recorded by the ATLAS experiment at the LHC. The results are based on 2250 W → ℓν and 179 Z/γ* → ℓℓ candidate events selected from a data set corresponding to an integrated luminosity of approximately 320 nb-1. The measured total W and Z/γ*-boson production cross sections times the respective leptonic branching ratios for the combined electron and muon channels are σtot W. BR(W → ℓν) = 9.96± 0.23(stat)±0.50(syst)±1.10(lumi) nb and σtot Z/γ*. BR(Z/γ* → ℓℓ) = 0:82±0:06 (stat)±0:05 (syst)±0:09 (lumi) nb (within the invariant mass window 66 < mℓℓ < 116 GeV). The W/Z cross-section ratio is measured to be 11.7±0.9(stat)±0.4(syst). In addition, measurements of the W+ and W- production cross sections and of the lepton charge asymmetry are reported. Theoretical predictions based on NNLO QCD calculations are found to agree with the measurements.