A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton-proton collisions at centre-of-mass energies of 7 and 8TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron-muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb(-1) at root s = 7 TeV and about 20 fb(-1) at root s = 8TeV for each experiment. The combined cross-sections are determined to be 178.5 +/- 4.7 pb at root s = 7 TeV and 243.3(-5.9)(+6.0) pb at root s = 8TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined crosssections is determined to be R-8/7 = 1.363 +/- 0.032. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are m(t)(pole) = 173.4(-2.0)(+1.8) GeV and alpha s(m(Z)) = 0.1170(-0.0018)(+0.0021).