The combination of measurements of the W boson polarization in top quark decays performed by the ATLAS and CMS collaborations is presented. The measurements are based on proton-proton collision data produced at the LHC at a centre-of-mass energy of 8 TeV, and corresponding to an integrated luminosity of about 20 fb(-1)for each experiment. The measurements used events containing one lepton and having different jet multiplicities in the final state. The results are quoted as fractions of W bosons with longitudinal (F-0), left-handed (F-L), or right-handed (F-R) polarizations. The resulting combined measurements of the polarization fractions are F-0= 0.693 +/- 0.014 and F-L= 0.315 +/- 0.011. The fractionF(R)is calculated from the unitarity constraint to be F-R=-0.008 +/- 0.007. These results are in agreement with the standard model predictions at next-to-next-to-leading order in perturbative quantum chromodynamics and represent an improvement in precision of 25 (29)% for F-0(F-L) with respect to the most precise single measurement. A limit on anomalous right-handed vector (V-R), and left- and right-handed tensor (g(L), g(R)) tWb couplings is set while fixing all others to their standard model values. The allowed regions are [-0.11,0.16] for V-R, [-0.08,0.05] for g(L), and [-0.04,0.02] for g(R), at 95% confidence level. Limits on the corresponding Wilson coefficients are also derived.