A measurement of the mass of the Higgs boson combining the $H\to ZZ^{*} \to 4\ell$ and $H\toγγ$ decay channels is presented. The result is based on 140 fb$^{-1}$ of proton-proton collision data collected by the ATLAS detector during LHC Run 2 at a centre-of-mass energy of 13 TeV combined with the Run 1 ATLAS mass measurement, yielding a Higgs boson mass of 125.11 $±$ 0.09 (stat.) $±$ 0.06 (syst.) = 125.11 $±$ 0.11 GeV. This corresponds to a 0.09 % precision achieved on this fundamental parameter of the Standard Model of particle physics.