A search for Higgs boson production in association with a W or Z boson, in the H→WW* 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 = 7TeV and 8TeV, 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 WH 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 WH 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 WH and ZH production modes are also combined with the gluon fusion and vector boson fusion production modes studied in the H → WW* → ℓvℓv 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 (KV) and fermions (KF); the combined results are: |KV| = 1.06+0.10 −0.10, |KF| = 0.85+0.26 −0.20.