Abstract: This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zγ pair in association with two jets. The analysis uses 140 fb−1 of LHC proton-proton collision data taken at s√=13 TeV recorded by the ATLAS detector during the years 2015-2018. Events with a Z boson candidate decaying into either an e+e− or μ+μ− pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and a large rapidity gap between the two jets and is measured with an observed and expected significance well above five standard deviations. The fiducial pp→Zγjj cross-section for the electroweak production is measured to be 3.6 ± 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0−1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions.