We present the first observation in hadronic collisions of the electroweak production of vector boson pairs (VV, V=W, Z) where one boson decays to a dijet final state. The data correspond to 3.5  fb−1 of integrated luminosity of pp collisions at s√=1.96  TeV collected by the CDF II detector at the Fermilab Tevatron. We observe 1516±239(stat)±144(syst) diboson candidate events and measure a cross section σ(pp→VV+X) of 18.0±2.8(stat)±2.4(syst)±1.1(lumi)  pb, in agreement with the expectations of the standard model.