  Future precision measurements of Higgs boson decays will determine the
branching fraction for the decay into two photons with a precision at the one
percent level. To fully exploit such measurements, equally precise theoretical
predictions need to be available. To this end we compute four-loop QCD
corrections in the large top quark mass expansion to the Higgs boson--photon
form factor, which enter the two-photon decay width at
next-to-next-to-next-to-leading order. Furthermore we obtain corrections to the
two-photon decay width stemming from the emission of additional gluons, which
contribute for the first time at next-to-next-to-leading order. Finally, we
combine our results with other available perturbative corrections and estimate
the residual uncertainty due to missing higher-order contributions.
