We present a search for the Higgs boson in final states with two oppositely charged leptons and large missing transverse energy as expected in H→WW→ℓνℓ′ν′ decays. The events are selected from the full Run II data sample of 9.7 fb-1 of pp¯ collisions collected with the D0 detector at the Fermilab Tevatron Collider at s=1.96 TeV. To validate our search methodology, we measure the nonresonant WW production cross section and find σWW=11.6±0.7 pb, in agreement with the standard model prediction. In the Higgs boson search, no significant excess above the background expectation is observed. Upper limits at the 95% confidence level on the Higgs boson production cross section are therefore derived. Within the standard model, the Higgs boson mass range 159