This paper presents measurements of the polarization ofW bosons in top quark decays, derived from tt̄ events with missing transverse momentum, one charged lepton and at least four jets, or two charged leptons and at least two jets. Data from pp collisions at a centre-of-mass energy of 7 TeV were collected with the ATLAS experiment at the LHC and correspond to an integrated luminosity of 1.04 fb-1. The measured fractions of longitudinally, left- and right-handed polarization are F0 = 0.67 ± 0.07, FL = 0.32 ± 0.04 and FR = 0.01 ± 0.05, in agreement with the Standard Model predictions. As the polarization of the W bosons in top quark decays is sensitive to the Wtb vertex Lorentz structure and couplings, the measurements were used to set limits on anomalous contributions to the Wtb couplings. © CERN.