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, μ V H , is found to be μ V H  = 3.0 − 1.1 + 1.3 (stat.) − 0.7 + 1.0 (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 μ ggF + VBF + VH  = 1. 16 − 0.15 + 0.16 (stat.) − 0.15 + 0.18 (sys.). The results are interpreted in terms of scaling factors of the Higgs boson couplings to vector bosons ( κ V ) and fermions ( κ F ); the combined results are: | κ V | = 1.06 − 0.10 + 0.10 , | κ F | = 0. 85 − 0.20 + 0.26 .