This Letter presents a constraint on the total width of the Higgs boson (\(\Gamma_H\)) using a combined measurement of on-shell Higgs boson production and the production of four top quarks, which involves contributions from off-shell Higgs boson-mediated processes. This method relies on the assumption that the tree-level Higgs-top Yukawa coupling strength is the same for on-shell and off-shell Higgs boson production processes. The result is based on up to 140 fb\(^{-1}\) of proton-proton collisions at a centre-of-mass energy of \(\sqrt{s}\) = 13 TeV collected with the ATLAS detector at the Large Hadron Collider. The observed (expected) 95% confidence level upper limit on \(\Gamma_H\) is 450 MeV (75 MeV). Additionally, considering the constraint on the Higgs-top Yukawa coupling from loop-induced Higgs boson production and decay processes further yields an observed (expected) upper limit of 160 MeV (55 MeV).