We present a study of B→X(3872)K with X(3872) decaying to D*0D̄0 using a sample of 657×106 BB̄ pairs recorded at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. Both D*0→D0γ and D*0→D0π0 decay modes are used. We find a peak of 50.1-11.1+14.8 events with a mass of (3872.9-0.4-0.5+0.6+0.4)MeV/c2, a width of (3.9-1.4-1.1+2.8+0.2)MeV/c2 and a product branching fraction B(B→X(3872)K)×B(X(3872)→D*0D̄0)=(0. 80±0.20±0.10)×10-4, where the first errors are statistical and the second ones are systematic. The significance of the signal is 6.4σ. The difference between the fitted mass and the D*0D̄0 threshold is calculated to be (1.1-0.4-0.3+0.6+0.1)MeV/c2. We also obtain an upper limit on the product of branching fractions B(B→Y(3940)K) ×B(Y(3940)→D*0D̄0) of 0.67×10 -4 at 90% CL.