This Letter presents results from a combination of searches for Higgs boson pair production using 126-140  fb^{-1} of proton-proton collision data at sqrt[s]=13  TeV recorded with the ATLAS detector. At 95% confidence level (CL), the upper limit on the production rate is 2.9 times the standard model (SM) prediction, with an expected limit of 2.4 assuming no Higgs boson pair production. Constraints on the Higgs boson self-coupling modifier κ_{λ}=λ_{HHH}/λ_{HHH}^{SM}, and the quartic HHVV coupling modifier κ_{2V}=g_{HHVV}/g_{HHVV}^{SM}, are derived individually, fixing the other parameter to its SM value. The observed 95% CL intervals are -1.2<κ_{λ}<7.2 and 0.6<κ_{2V}<1.5, respectively, while the expected intervals are -1.6<κ_{λ}<7.2 and 0.4<κ_{2V}<1.6 in the SM case. Constraints obtained for several interaction parameters within Higgs effective field theory are the strongest to date, offering insights into potential deviations from SM predictions.