  We present the quantum chromodynamics (QCD) corrections for Higgs boson
decays to hadronic final states at next-to-next-to-next-to-leading order
(N$^3$LO) in the strong coupling constant $\alpha_s$. In particular, we
consider the Higgs boson decay to massless bottom quarks and the Higgs boson
decay to a pair of gluons in the limit of a heavy top quark. The tree-level
five-parton, the one-loop four-parton, the two-loop three-parton, and the
three-loop two-parton matrix elements are integrated separately over the
inclusive phase space and classified by partons appearing in the final state
and by colour structure. As a check, we reproduce known results for the
hadronic $R$-ratios at N$^3$LO. We study patterns of infrared singularity
cancellation within the colour layers of the integrated expressions and observe
an agreement in the highest trascendental weight terms in the decay of
different colour singlets to quarks. We anticipate that our result will be an
essential ingredient for the formulation of N$^3$LO subtraction schemes.
