Suppose $ngeq 3$ and let $B$ be the open unit ball in $mathbb{R}^n$. Let $varphi: Bto B$ be a $C^2$ map whose Jacobian does not change sign, and let $psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition operators $W_{varphi,psi}$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{varphi,psi}$ on $h^p(B)$ when $varphi$ is a Mobius transformation of $B$.
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