  We observe $D^0-\bar{D}^0$ mixing in the decay $D^0\rightarrow K^+\pi^-$
using a data sample of integrated luminosity 976 fb$^{-1}$ collected with the
Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. We measure the
mixing parameters ${x'}^2 = (0.09\pm0.22)\times 10^{-3}$ and $y' =
(4.6\pm3.4)\times 10^{-3}$ and the ratio of doubly Cabibbo-suppressed to
Cabibbo-favored decay rates $R_D = (3.53\pm0.13)\times 10^{-3}$, where the
uncertainties are statistical and systematic combined. Our measurement excludes
the no-mixing hypothesis at the 5.1 standard deviation level.
