We present a study of B0→Ds*+π- and B0→Ds*-K+ decays based on a sample of 657×106 BB̄ events collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. We measure the branching fractions to be B(B0→Ds*+π-)=(1.75±0.34(stat)±0.17(syst) ±0.11(B))×10-5 and B(B0→Ds*-K +)=(2.02±0.33(stat)±0.18(syst)±0.13(B)) ×10-5, with significances of 6.1 and 8.0 standard deviations, respectively. The first uncertainty is statistical, the second is due to the experimental systematics, and the third is from uncertainties in the Ds+ decay branching fractions. From our measurements, we obtain the most precise determination so far of RD*π, where RD*π is the ratio between amplitudes of the doubly Cabibbo-suppressed decay B0→D*+π- and the Cabibbo-favored B0→D*-π+ decay. © 2010 The American Physical Society.