Measurements of production cross sections of (\text{W}\text{Z}) and same-sign (\text{W}\text{W}) boson pairs in association with two jets in proton-proton collisions at (\sqrt{s}=13\phantom{\rule{0.2em}{0ex}}\text{TeV}) at the LHC are reported. The data sample corresponds to an integrated luminosity of 137(\phantom{\rule{0.2em}{0ex}}{\text{fb}}^{-1}), collected with the CMS detector during 2016–2018. The measurements are performed in the leptonic decay modes Image 1 and Image 2, where (\ell,{\ell }^{\prime }=\text{e}), Image 3. Differential fiducial cross sections as functions of the invariant masses of the jet and charged lepton pairs, as well as of the leading-lepton transverse momentum, are measured for ({\text{W}}^{±}{\text{W}}^{±}) production and are consistent with the standard model predictions. The dependence of differential cross sections on the invariant mass of the jet pair is also measured for (\text{W}\text{Z}) production. An observation of electroweak production of (\text{W}\text{Z}) boson pairs is reported with an observed (expected) significance of 6.8 (5.3) standard deviations. Constraints are obtained on the structure of quartic vector boson interactions in the framework of effective field theory.