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 fraction (F_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.