A search for Higgs boson production in association with a W or Z boson, in the H→ W W∗ decay channel, is performed with a data sample collected with the ATLAS detector at the LHC in proton-proton collisions at centre-of-mass energies s√=7 TeV and 8 TeV, corresponding to integrated luminosities of 4.5 fb−1 and 20.3 fb−1, respectively. The WH production mode is studied in two-lepton and three-lepton final states, while two- lepton and four-lepton final states are used to search for the ZH production mode. The observed significance, for the combined W H and ZH production, is 2.5 standard deviations while a significance of 0.9 standard deviations is expected in the Standard Model Higgs boson hypothesis. The ratio of the combined W H and ZH signal yield to the Standard Model expectation, μV H , is found to be μV H = 3.0 + 1.3− 1.1 (stat.) + 1.0− 0.7 (sys.) for the Higgs boson mass of 125.36 GeV. The W H and ZH production modes are also combined with the gluon fusion and vector boson fusion production modes studied in the H → W W∗ → ℓνℓν decay channel, resulting in an overall observed significance of 6.5 standard deviations and μggF + VBF + VH = 1. 16 + 0.16− 0.15 (stat.) + 0.18− 0.15 (sys.). The results are interpreted in terms of scaling factors of the Higgs boson couplings to vector bosons (κV ) and fermions (κF ); the combined results are: |κV| = 1.06 + 0.10− 0.10 , |κF| = 0. 85 + 0.26− 0.20 .