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This analysis presents an observation of the photon-fusion production of W boson pairs using the CMS detector at the LHC. The total cross section of the W+W− production in photon fusion is measured using proton-proton collision data with an integrated luminosity of 138 fb−1 collected with the CMS detector in 2016–2018 at a center-of-mass energy of s=13 TeV. Events are selected in the final state with one isolated electron and one isolated muon, and no additional tracks associated with the electron-muon production vertex. The total and fiducial production cross sections are 643−78+82 fb and 3.96−0.51+0.53 fb, respectively, in agreement with the standard model predictions of 631 ± 126 fb and 3.87 ± 0.77 fb. This agreement enables stringent constraints on anomalous quartic gauge couplings within a dimension-8 effective field theory framework.