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 8 TeV 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 $ \sqrt{s} $ = 7 TeV and about 20 fb$^{−1}$ at $ \sqrt{s} $ = 8 TeV for each experiment. The combined cross-sections are determined to be 178.5 ± 4.7 pb at $ \sqrt{s} $ = 7 TeV and $ {243.3}_{-5.9}^{+6.0} $ pb at $ \sqrt{s} $ = 8 TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections 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^{\textrm{pole}}={173.4}_{-2.0}^{+1.8} $ GeV and $ {\alpha}_{\textrm{s}}\left({m}_Z\right)={0.1170}_{-0.0018}^{+0.0021} $.