This paper presents combinations of inclusive and differential measurements of the charge asymmetry (AC) in top quark pair (tt¯) 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 CHC7  = 0.005 ± 0.007 (stat) ± 0.006(syst) at 7 TeV and A C CHC8  = 0.0055 ± 0.0023 (stat) ± 0.0025 (syst) at 8 TeV. These values, as well as the combination of AC measurements as a function of the invariant mass of the tt¯ system at 8 TeV, are consistent with the respective standard model predictions.