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 (F0), left-handed (FL), or right-handed (FR) polarizations. The resulting combined measurements of the polarization fractions are F0 = 0.693 +- 0.014 and FL = 0.315 +- 0.011. The fraction FR is calculated from the unitarity constraint to be FR = −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 F0 (FL) with respect to the most precise single measurement. A limit on anomalous right-handed vector (VR), and left- and right-handed tensor (gL, gR) tWb couplings is set while fixing all others to their standard model values. The allowed regions are [−0.11, 0.16] for VR, [−0.08, 0.05] for gL, and [−0.04, 0.02] for gR, at 95% confidence level. Limits on the corresponding Wilson coefficients are also derived.