A measurement of off-shell Higgs boson production is performed in the H* → WW channel. The measurement uses a proton–proton collision dataset with an integrated luminosity of 140 fb−1 collected at a centre-of-mass energy of 13 TeV by the ATLAS detector at the Large Hadron Collider. Final states in which both W bosons decay leptonically are targeted, and events are categorised based on the flavour of the final-state leptons, the jet multiplicity, and the output of neural network-based classifiers. The data are found to be compatible with the Standard Model expectation. An observed (expected) upper bound on the 95 % symmetric confidence level interval is set on the rate of off-shell Higgs boson production at a value of 3.4 (4.4) times the Standard Model prediction. These results are combined with the results from the measurement of on-shell Higgs boson production in the same final states to obtain an observed (expected) upper bound at 95 % confidence level on the Higgs boson total width of 13.1 (17.3) MeV.