This paper presents measurements of the polarization of W bosons in top quark decays, derived from tt¯ 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 F 0 = 0.67 ± 0.07, F L = 0.32 ± 0.04 and F R = 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.