  In this paper, we prove that complete gradient steady K\"ahler-Ricci solitons
with harmonic Bochner tensor are necessarily K\"ahler-Ricci flat, i.e.,
Calabi-Yau, and that complete gradient shrinking (or expanding) K\"ahler-Ricci
solitons with harmonic Bochner tensor must be isometric to a quotient of
$N^k\times \mathbb{C}^{n-k}$, where $N$ is a K\"ahler-Einstein manifold with
positive (or negative) scalar curvature.
