A bstract The total and differential Higgs boson production cross-sections are measured through a combined statistical analysis of the H → ZZ * → 4 ℓ and H → γγ decay channels. The results are based on a dataset of 139 fb − 1 of proton–proton collisions at a centre-of-mass energy of 13 TeV, recorded by the ATLAS detector at the Large Hadron Collider. The measured total Higgs boson production cross-section is $$ {55.5}_{-3.8}^{+4.0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mn>55.5</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3.8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>4.0</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> pb, consistent with the Standard Model prediction of 55 . 6 ± 2 . 5 pb. All results from the two decay channels are compatible with each other, and their combination agrees with the Standard Model predictions. A combined statistical interpretation of the measured fiducial cross-sections as a function of the Higgs boson transverse momentum is performed in order to probe the Yukawa couplings to the bottom and charm quarks. A similar interpretation is performed by including also the constraints from the measurements of Higgs boson production in association with a W or Z boson in the H → $$ b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and $$ c\overline{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>c</mml:mi> <mml:mover> <mml:mi>c</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> decay channels.