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 36.1 fb⁻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. © 2019 The Author(s)