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 $ \sqrt{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$_{− 0.20}^{+ 0.26}$
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