We report a measurement of resonance parameters of the orbitally excited (L=1) narrow B0 mesons in decays to B(*)+π− using 1.7  fb−1 of data collected by the CDF II detector at the Fermilab Tevatron. The mass and width of the B*02 state are measured to be m(B*02)=5740.2+1.7−1.8(stat)+0.9−0.8(syst)  MeV/c2 and Γ(B*02)=22.7+3.8−3.2(stat)+3.2−10.2(syst)  MeV/c2. The mass difference between the B*02 and B01 states is measured to be 14.9+2.2−2.5(stat)+1.2−1.4(syst)  MeV/c2, resulting in a B01 mass of 5725.3+1.6−2.2(stat)+1.4−1.5(syst)  MeV/c2. This is currently the most precise measurement of the masses of these states and the first measurement of the B*02 width.