We report the observation of the production of the Higgs boson in its decay to $WW^\ast$, based on an excess over background in the dilepton final state of $6.1$ standard deviations, where the standard model expectation is $5.8$ standard deviations. Evidence for the vector-boson fusion (VBF) production process is obtained with a significance of $3.2$ standard deviations. The results are obtained from a data sample corresponding to an integrated luminosity of 25~\textrm{pb}^{-1} from $\sqrt{s}=7$ and $8$\,TeV $pp$ collisions recorded by the ATLAS detector at the LHC. For a Higgs-boson mass of $125.36$ GeV, the ratio of the observed to expected values of the total production cross section times branching fraction is 1.08^{+0.16}_{-0.15}~\textrm{(stat.)}^{+0.16}_{-0.13}~\textrm{(syst.)}. The corresponding ratios for the gluon-gluon fusion and vector-boson fusion production mechanisms are 1.01\pm 0.19~\textrm{(stat.)}^{+0.20}_{-0.17}~\textrm{(syst.)} and 1.28^{+0.44}_{-0.40}~\textrm{(stat.)}^{+0.29}_{-0.21}~\textrm{(syst.)}, respectively. At $\sqrt{s}=8$ TeV the total production cross sections are measured to be \sigma(gg\to~H\rightarrow WW^\ast) = 4.6\pm0.9\,\textrm{(stat.)}\,^{+0.8}_{-0.7}\,\textrm{(syst.)}\textrm{pb} and \sigma(\textrm{VBF}~H\rightarrow WW^\ast) = 0.51\,^{+0.17}_{-0.15}\,\textrm{(stat.)}\,^{+0.13}_{-0.08}\,\textrm{(syst.)}\textrm{pb}. The fiducial cross section is determined for the gluon-gluon fusion process in exclusive final states with zero or one associated jet.

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