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