  We define positive Toeplitz operators between weighted harmonic Bloch spaces
$b^\infty_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full range of
parameter $\alpha\in\mathbb{R}$. We give characterizations of bounded and
compact Toeplitz operators taking one weighted harmonic Bloch space into
a\-not\-her in terms of Carleson and vanishing Carleson measures.
