The inclusive cross section for the production of a single top quark in association with a W boson is measured using 140 fb-1 of proton-proton collision data collected with the ATLAS detector at s=13 TeV. Events containing two charged leptons and at least one jet identified as originating from a b-quark are selected. A multivariate discriminant is constructed to separate the tW signal from the tt¯ background. The cross section is extracted using a profile likelihood fit to the signal and control regions and it is measured to be σtW=75-14+15 pb, in good agreement with the Standard Model prediction. The measured cross section is used to extract a value for the left-handed form factor at the Wtb vertex times the Cabibbo-Kobayashi-Maskawa matrix element |fLVVtb| of 0.97±0.10.