This paper presents the combinations of single-top-quark production cross-section measurements by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at $ \sqrt{s} $ = 7 and 8 TeV corresponding to integrated luminosities of 1.17 to 5.1 fb$^{−1}$ at $ \sqrt{s} $ = 7 TeV and 12.2 to 20.3 fb$^{−1}$ at $ \sqrt{s} $ = 8 TeV. These combinations are performed per centre-of-mass energy and for each production mode: t-channel, tW, and s-channel. The combined t-channel cross-sections are 67.5 ± 5.7 pb and 87.7 ± 5.8 pb at $ \sqrt{s} $ = 7 and 8 TeV respectively. The combined tW cross-sections are 16.3 ± 4.1 pb and 23.1 ± 3.6 pb at $ \sqrt{s} $ = 7 and 8 TeV respectively. For the s-channel cross-section, the combination yields 4.9 ± 1.4 pb at $ \sqrt{s} $ = 8 TeV. The square of the magnitude of the CKM matrix element V${tb}$ multiplied by a form factor f${LV}$ is determined for each production mode and centre-of-mass energy, using the ratio of the measured cross-section to its theoretical prediction. It is assumed that the top-quark-related CKM matrix elements obey the relation |V${td}$|, |V${ts}$| ≪ |V${tb}$|. All the |f${LV}$V${tb}$|$^{2}$ determinations, extracted from individual ratios at $ \sqrt{s} $ = 7 and 8 TeV, are combined, resulting in |f${LV}$V$_{tb}$| = 1.02 ± 0.04 (meas.) ± 0.02 (theo.). All combined measurements are consistent with their corresponding Standard Model predictions.