We consider the Boussinesq equations in either an exterior domain in$\mathbb{R}^{n}$, the whole space $\mathbb{R}^{n}$, the half space$\mathbb{R}_{+}^{n}$ or a bounded domain in $\mathbb{R}^{n}$, wherethe dimension $n$ satisfies $n \geq 3$. We give a class of stablesteady solutions, which improves and complements the previousstability results. Our results give a complete answer to thestability problem for the Boussinesq equations in weak-$L^{p}$spaces, in the sense that we only assume that the stable steadysolution belongs to scaling invariant class $L_{\sigma}^{(n,\infty)}\times L^{(n,\infty)}$. Moreover, some considerationsabout the exponential decay (in bounded domains) and the uniquenessof the disturbance are done.