A combined measurement of differential and inclusive total cross sections of Higgs boson production is performed using 36.1 fb$^{-1}$ of 13 TeV proton-proton collision data produced by the LHC and recorded by the ATLAS detector in 2015 and 2016. Cross sections are obtained from measured $H \rightarrow γγ$ and $H \rightarrow ZZ^* \rightarrow 4\ell$ event yields, which are combined taking into account detector efficiencies, resolution, acceptances and branching fractions. The total Higgs boson production cross section is measured to be 57.0$^{+6.0}_{-5.9}$ (stat.) $^{+4.0}_{-3.3}$ (syst.) pb, in agreement with the Standard Model prediction. Differential cross-section measurements are presented for the Higgs boson transverse momentum distribution, Higgs boson rapidity, number of jets produced together with the Higgs boson, and the transverse momentum of the leading jet. The results from the two decay channels are found to be compatible, and their combination agrees with the Standard Model predictions.