For quantizable compact Kähler manifolds with associated quantum line bundle the Berezin transform for functions is introduced. This is a generalization of the original transform between contravariant and covariant Berezin symbols. If one considers all positve tensor powers of and the Berezin transform then it admits a complete asymptotic expansion in powers of , e.g. with differential operators . It turns out that and , the Laplace-Beltrami operator. Consequences of this expansion for the Berezin-Toeplitz operator quantization and the Berezin-Toeplitz deformation quantization are discussed.