The mass of the Higgs boson is measured in the H→γγ decay channel, exploiting the high resolution of the invariant mass of photon pairs reconstructed from the decays of Higgs bosons produced in proton–proton collisions at a centre-of-mass energy s=13 TeV. The dataset was collected between 2015 and 2018 by the ATLAS detector at the Large Hadron Collider, and corresponds to an integrated luminosity of 140 fb⁻¹. The measured value of the Higgs boson mass is 125.17±0.11(stat.)±0.09(syst.) GeV and is based on an improved energy scale calibration for photons, whose impact on the measurement is about four times smaller than in the previous publication. A combination with the corresponding measurement using 7 and 8 TeV pp collision ATLAS data results in a Higgs boson mass measurement of 125.22±0.11(stat.)±0.09(syst.) GeV. With an uncertainty of 1.1 per mille, this is currently the most precise measurement of the mass of the Higgs boson from a single decay channel.