This paper presents combinations of inclusive and differential measurements of the charge asymmetry ((A_C)) in top quark pair (\left(t\overline{t}\right)) events with a lepton+jets signature by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. The data correspond to integrated luminosities of about 5 and 20 fb⁻¹ for each experiment, respectively. The resulting combined LHC measurements of the inclusive charge asymmetry are (A_C^{LHC7}) = 0.005 ± 0.007 (stat) ± 0.006(syst) at 7 TeV and (A_C^{LHC8}) = 0.0055 ± 0.0023 (stat) ± 0.0025 (syst) at 8 TeV. These values, as well as the combination of ((A_C)) measurements as a function of the invariant mass of the (t\overline{t}) system at 8 TeV, are consistent with the respective standard model predictions.