A bstract This paper presents measurements of the polarization of W bosons in top quark decays, derived from $ t\overline t $ 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.