We study the e+e-→γωJ/ψ process using 11.6 fb-1 e+e- annihilation data taken at center-of-mass energies from 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 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/c2 and a width of 115-26+38±12 MeV. In addition, to describe the ωJ/ψ mass distribution above 3.9 GeV/c2, 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.