We report on a Dalitz plot analysis of B-→D+π-π- decays, based on a sample of about 383×106 Υ(4S)→BB̅ decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We find the total branching fraction of the three-body decay: B(B-→D+π-π-)=(1.08±0.03±0.05)×10-3. We observe the established D2*0 and confirm the existence of D0*0 in their decays to D+π-, where the D2*0 and D0*0 are the 2+ and 0+cu̅ P-wave states, respectively. We measure the masses and widths of D2*0 and D0*0 to be: mD2*0=(2460.4±1.2±1.2±1.9) MeV/c2, ΓD2*0=(41.8±2.5±2.1±2.0) MeV, mD0*0=(2297±8±5±19) MeV/c2, and ΓD0*0=(273±12±17±45) MeV. The stated errors reflect the statistical and systematic uncertainties, and the uncertainty related to the assumed composition of signal events and the theoretical model.