The mass of the Higgs boson is measured in the 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. The measured value of the Higgs boson mass is GeV and is based on improved momentum-scale calibration for muons relative to 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 collision data, resulting in a Higgs boson mass measurement of GeV.