This paper presents a measurement of the W+W¯ production cross section in pp collisions at √s = 7 TeV. The leptonic decay channels are analyzed using data corresponding to an integrated luminosity of 4.6 fb-1 collected with the ATLAS detector at the Large Hadron Collider. The W+W¯ production cross section σ(pp→W+W¯+X) is measured to be 51.9 ± 2.0 (stat) ± 3.9 (syst) ± 2.0 (lumi) pb, compatible with the Standard Model prediction of 44.7+2.1-1.9 pb. A measurement of the normalized fiducial cross section as a function of the leading lepton transverse momentum is also presented. The reconstructed transverse momentum distribution of the leading lepton is used to extract limits on anomalous WWZ and WWγ couplings.