Using a sample of $(1310.6\pm 7.0)\times {10}^6$ $J/\psi$ events recorded with the Beijing Spectrometer III detector at the Beijing Electron Positron Collider II, we report the observation of the decay of the $\left(1^1{S}_0\right)$ charmonium state ${\eta }_c$ into a pair of $\omega$ mesons in the process $J/\psi \to \gamma \omega \omega$. The branching fraction is measured for the first time to be $B({\eta }_c\to \omega \omega )=(2.88\pm 0.10\pm 0.46\pm 0.68)\times {10}^{-3}$, where the first uncertainty is statistical, the second systematic, and the third is from the uncertainty of $B(J/\psi \to \gamma {\eta }_c)$. The mass and width of the ${\eta }_c$ are determined as $M=(2985.9\pm 0.7\pm 2.1)\mathrm{MeV}/c^2$ and $\Gamma =(33.8\pm 1.6\pm 4.1)\mathrm{MeV}$.