We present a study of B→X(3872)K with X(3872) decaying to D0D̄0 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 D0→D0γ and D0→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)→D0D̄0)=(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 D0D̄0 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)→D0D̄0) of 0.67×10 -4 at 90% CL. © 2010 The American Physical Society.