We study the e^{+}e^{-}→γωJ/ψ process using 11.6 fb^{-1} e^{+}e^{-} annihilation data taken at center-of-mass energies from sqrt[s]=4.008 GeV to 4.600 GeV with the BESIII detector at the BEPCII storage ring. The X(3872) resonance is observed for the first time in the ωJ/ψ system with a significance of more than 5σ. The relative decay ratio of X(3872)→ωJ/ψ and π^{+}π^{-}J/ψ is measured to be R=1.6_{-0.3}^{+0.4}±0.2, where the first uncertainty is statistical and the second systematic (the same hereafter). The sqrt[s]-dependent cross section of e^{+}e^{-}→γX(3872) is also measured and investigated, and it can be described by a single Breit-Wigner resonance, referred to as the Y(4200), with a mass of 4200.6_{-13.3}^{+7.9}±3.0 MeV/c^{2} and a width of 115_{-26}^{+38}±12 MeV. In addition, to describe the ωJ/ψ mass distribution above 3.9 GeV/c^{2}, we need at least one additional Breit-Wigner resonance, labeled as X(3915), in the fit. The mass and width of the X(3915) are determined. The resonant parameters of the X(3915) agree with those of the Y(3940) in B→KωJ/ψ and of the X(3915) in γγ→ωJ/ψ observed by the Belle and BABAR experiments within errors.