We report two complementary measurements of the WW+WZ cross section in the final state consisting of an electron or muon, missing transverse energy, and jets, performed using pp collision data at s√=1.96  TeV collected by the CDF II detector. The first method uses the dijet invariant mass distribution while the second more sensitive method uses matrix-element calculations. The result from the second method has a signal significance of 5.4σ and is the first observation of WW+WZ production using this signature. Combining the results gives σWW+WZ=16.0±3.3  pb, in agreement with the standard model prediction.