A combination of fifteen top quark mass measurements performed by the ATLAS and CMS experiments at the LHC is presented. The datasets used correspond to an integrated luminosity of up to 5 and $20{\mathrm{fb}}^{-1}$ of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, respectively. The combination includes measurements in top quark pair events that exploit both the semileptonic and hadronic decays of the top quark, and a measurement using events enriched in single top quark production via the electroweak $t$ channel. The combination accounts for the correlations between measurements and achieves an improvement in the total uncertainty of 31% relative to the most precise input measurement. The result is $m_t=172.52\pm 0.14\left(\mathrm{stat}\right)\pm 0.30\left(\mathrm{syst}\right)\mathrm{GeV}$, with a total uncertainty of 0.33 GeV.