  Based on a sample of \etapr mesons produced in the radiative decay
$J/\psi\to\gamma\eta^{\prime}$ in $1.31\times 10^9$ $J/\psi$ events collected
with the BESIII detector, the decay $\eta^{\prime}\to\omega e^{+} e^{-}$ is
observed for the first time, with a statistical significance of $8\sigma$. The
branching fraction is measured to be $\mathcal{B}(\eta^{\prime}\to\omega e^{+}
e^{-})=(1.97\pm0.34(\text{stat})\pm0.17(\text{syst}))\times10^{-4}$, which is
in agreement with theoretical predictions. The branching fraction of
$\eta^{\prime}\to\omega\gamma$ is also measured to be
$(2.55\pm0.03(\text{stat})\pm0.16(\text{syst}))\times10^{-2}$, which is the
most precise measurement to date, and the relative branching fraction
$\frac{\mathcal{B}(\eta^{\prime}\to \omega
e^{+}e^{-})}{\mathcal{B}(\eta^{\prime}\to \omega \gamma)}$ is determined to be
$(7.71\pm1.34(\text{stat})\pm0.54(\text{syst}))\times10^{-3}$.
