A combination of measurements of the CP properties of Higgs boson interactions with electroweak gauge bosons is presented, using 140 fb^{-1} of proton-proton collisions at sqrt[s]=13 TeV recorded by the ATLAS detector. Results from vector boson fusion H→ττ/WW^{*}/γγ, inclusive H→ZZ^{*}, and WH,H→bb[over ¯] channels are combined. No evidence of CP violation is observed, and constrains on the CP-violating operators in the Standard Model effective field theory framework (SMEFT) are set in the Warsaw basis. The results from the combination improve by over 40% on previous individual limits on c_{HW[over ˜]} and, for the first time, simultaneous constraints on three coefficients c_{HW[over ˜]}, c_{HB[over ˜]}, and c_{HW[over ˜]B} are set. These limits are the most stringent constraints to date on the relevant Wilson coefficients in the SMEFT framework with minimum model dependence.