The mass of the Higgs boson is measured in the H→ZZ⁎→4ℓ decay channel. The analysis uses proton–proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector between 2015 and 2018, corresponding to an integrated luminosity of 139 fb⁻¹. The measured value of the Higgs boson mass is 124.99±0.18(stat.)±0.04(syst.) GeV. In final states with muons, this measurement benefits from an improved momentum-scale calibration relative to that adopted in previous publications. The measurement also employs an analytic model that takes into account the invariant-mass resolution of the four-lepton system on a per-event basis and the output of a deep neural network discriminating signal from background events. This measurement is combined with the corresponding measurement using 7 and 8 TeV pp collision data, resulting in a Higgs boson mass of 124.94±0.17(stat.)±0.03(syst.) GeV.