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.