An observation of electroweak W^±Z production in association with two jets in proton–proton collisions is presented. The data collected by the ATLAS detector at the Large Hadron Collider in 2015 and 2016 at a centre-of-mass energy of s=13 TeV are used, corresponding to an integrated luminosity of 36.1fb⁻¹. Events containing three identified leptons, either electrons or muons, and two jets are selected. The electroweak production of W^±Z bosons in association with two jets is measured with an observed significance of 5.3 standard deviations. A fiducial cross-section for electroweak production including interference effects and for a single leptonic decay mode is measured to be σ_WZjj−EW=0.57_−0.13 ^+0.14(stat.)_−0.06 ^+0.07(syst.)fb. Total and differential fiducial cross-sections of the sum of W^±Zjj electroweak and strong productions for several kinematic observables are also measured.