Constraints on the Higgs boson self-coupling are set by combining double-Higgs boson analyses in the bb¯bb¯, bb¯τ+τ− and bb¯γγ decay channels with single-Higgs boson analyses targeting the γγ, ZZ⁎, WW⁎, τ+τ− and bb¯ decay channels. The data used in these analyses were recorded by the ATLAS detector at the LHC in proton–proton collisions at s=13 TeV and correspond to an integrated luminosity of 126–139 fb⁻¹. The combination of the double-Higgs analyses sets an upper limit of μHH<2.4 at 95% confidence level on the double-Higgs production cross-section normalised to its Standard Model prediction. Combining the single-Higgs and double-Higgs analyses, with the assumption that new physics affects only the Higgs boson self-coupling (λHHH), values outside the interval −0.4<κλ=(λHHH/λHHHSM)<6.3 are excluded at 95% confidence level. The combined single-Higgs and double-Higgs analyses provide results with fewer assumptions, by adding in the fit more coupling modifiers introduced to account for the Higgs boson interactions with the other Standard Model particles. In this relaxed scenario, the constraint becomes −1.4<κλ<6.1 at 95% CL.