Based on a sample of η′ mesons produced in the radiative decay J/ψ→γη′ in 1.31×109 J/ψ events collected with the BESIII detector, the decay η′→ωe+e− is observed for the first time, with a statistical significance of 8σ. The branching fraction is measured to be B(η′→ωe+e−)=(1.97±0.34(stat)±0.17(syst))×10−4, which is in agreement with theoretical predictions. The branching fraction of η′→ωγ is also measured to be (2.55±0.03(stat)±0.16(syst))×10−2, which is the most precise measurement to date, and the relative branching fraction B(η′→ωe+e−)B(η′→ωγ) is determined to be (7.71±1.34(stat)±0.54(syst))×10−3.