  In this paper we prove that any complete conformal gradient soliton with
nonnegative Ricci tensor is either isometric to a direct product
$\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean
space $\mathbb{R}^{n}$ or to the round sphere $\mathbb{S}^{n}$. In particular,
we show that any complete, noncompact, gradient Yamabe-type soliton with
positive Ricci tensor is rotationally symmetric, whenever the potential
function is nonconstant.
